Find the equation of the circle whose center and radius are given. center ( -2, -5), radius = 1

QUESTION POSTED AT 18/01/2020 - 07:04 AM

Answered by admin AT 18/01/2020 - 07:04 AM

Answer:  The required equation of the circle is x^2+y^2+4x+10y+28=0.

Step-by-step explanation:  We are given to find the equation of the circle with center (-2, -5) and radius of length 1 unit.

We know that

the standard equation of a circle with center (h, k) and radius of length r units is given by

(x-h)^2+(y-k)^2=r^2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)

For the given circle, we have

center, (h, k) = (-2, -5)   and  radius, r = 1 units.

Therefore, from equation (i), we get

(x-(-2))^2+(y-(-5))^2=1^2\\\\\Rightarrow (x+2)^2+(y+5)^2=1\\\\\Rightarrow x^2+4x+4+y^2+10x+25=1\\\\\Rightarrow x^2+y^2+4x+10y+29-1=0\\\\\Rightarrow x^2+y^2+4x+10y+28=0.

Thus, the required equation of the circle is x^2+y^2+4x+10y+28=0.

Post your answer

Related questions

5. What is an equation for the line with slope and y-intercept 9? (1 point) y = x y = 9x y = x + 9 y = 9x +  6. What is an equation in slope-intercept form for the line that passes through the points (1, –3) and (3, 1)? (1 point) y = 3x + 1 y = x – 3 y = 2x + 5 y = 2x – 5

6.) y - (-3) = (1 - (-3))/(3 - 1) (x - 1)
y + 3 = (1 + 3)/2 (x - 1)
y + 3 = 4/2 (x - 1)
y + 3 = 2(x - 1) = 2x - 2
y = 2x - 2 - 3 = 2x - 5
y = 2x - 5

ANSWERED AT 16/02/2020 - 07:04 PM


QUESTION POSTED AT 16/02/2020 - 07:04 PM

Find the area of the regular polygon. Give the answer to the nearest tenth. dodecagon with a perimeter of 108 cm ...?

A regular dodecagon is a polygon with 12 equal sides.
Length of each side = 108/12 = 9 cm.

Length of the apothem = (9/2)/tan 15 = 9/2tan 15 = 16.79 cm

Area of each triangle = 9/2(16.79) = 75.57 cm^2

Therefore, area of the dodecagon = 12(75.57) = 906.9 cm^2

ANSWERED AT 16/02/2020 - 06:36 PM


QUESTION POSTED AT 16/02/2020 - 06:36 PM

Write a proportion that can be used to find the cost of 10 notebooks if 3 notebooks cost $1.98.

The solution to the problem is as follows:


For 3 notebooks you pay $1.98 so the ratio is 1:0.66.
For 10 notebooks, then we could scale the ratio and it will become 10:6.60. So they will cost you $6.60.


I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

ANSWERED AT 16/02/2020 - 06:35 PM


QUESTION POSTED AT 16/02/2020 - 06:35 PM

Find two fractions with the difference of 1/5 but with neither denominator equal to 5

The two fractions with the difference of 1/5 but with neither denominator equal to 5 is 4/10 and 2/10.

ANSWERED AT 16/02/2020 - 06:32 PM


QUESTION POSTED AT 16/02/2020 - 06:32 PM

A rectangular table is two times as long as it is wide. If the area is 50ft^2, find the length and the width of the table.

10ftx5ft .........................................................................................................................................................................................................................................................................................

ANSWERED AT 16/02/2020 - 06:32 PM


QUESTION POSTED AT 16/02/2020 - 06:32 PM

State domain of -5 0 , -4 2, 0 10 , 3 16

The domain is another name for the values of x

In the points ( -5 , 0) , ( -4 , 2) , (0 , 10) , and (3 , 16)

-5, -4, 0, and 3 are the domains

ANSWERED AT 16/02/2020 - 06:23 PM


QUESTION POSTED AT 16/02/2020 - 06:23 PM

Given ghi with g(4 -3), H (-4, 2), and I (2, 4), find the perpendicular bisector of HI in standard form

GI is the bisector of the perpendicular bisector.

ANSWERED AT 16/02/2020 - 06:06 PM


QUESTION POSTED AT 16/02/2020 - 06:06 PM

Find two numbers whose sum is 30, and whose difference is 26

Yea umm Im not sure but 2, 28?

ANSWERED AT 16/02/2020 - 06:02 PM


QUESTION POSTED AT 16/02/2020 - 06:02 PM

Fill in the blank: To find the values of p, q, r and s, you should start by finding all factor ___ of the leading coefficiant and constant term. Then try them to determine which ones give you the correct product ...?

I can be wrong, but I think that the answer is: To find the values of p, q, r and s, you should start by finding all factor pairs of the leading coefficiant and constant term. 

ANSWERED AT 16/02/2020 - 05:35 PM


QUESTION POSTED AT 16/02/2020 - 05:35 PM

A manufacturer finds that the revenue generated by selling x units of a certain commodity is given by the function R(x) = 100x − 0.2x2, where the revenue R(x) is measured in dollars. What is the maximum revenue, and how many units should be manufactured to obtain this maximum? ...?

The extrema of a function happen when the derivative is equal to zero. So first we calculate the derivative:R′(x)=100−0.4x
And then we solve:0=100−0.4x
0.4x=100
x=250 units
Now we can substitute back into the original equation to calculate the revenue:R(250)=100(250)−0.2(2502)
R(250)=$12500

ANSWERED AT 16/02/2020 - 05:33 PM


QUESTION POSTED AT 16/02/2020 - 05:33 PM

One number is 3 less than twice another. If their sum is 39, find the numbers. Which of the following systems of equations represents the word problem? A.y = 2x - 3 and y = x + 39 B.y = 2x - 3 and x + y = 39 C.y = 2(x - 3) and x + y = 39 ...?

Let

y------> one number

x-----> another number

we know that

y=2x-3 ------> equation A

x+y=39 ------> equation B

substitute equation A in equation B

x+[2x-3]=39

3x=39+3

x=42/3=14

Find the value of y

y=2*14-3=25

the numbers are 25 and 14

therefore

the answer is the option B

y=2x-3 and x+y=39

ANSWERED AT 16/02/2020 - 05:32 PM


QUESTION POSTED AT 16/02/2020 - 05:32 PM

The medians of a triangle are the line segments from each vertex to the midpoint of the opposite side. Find the lengths of the medians of the triangle with vertices at A=(0,0), B=(6,0), C=(4,4) ...?

Answer:

\sqrt{29} , \sqrt{20} , \sqrt{17}

Step-by-step explanation:

Consider ΔABC with vertices A\left ( 0,0 \right )\,,\,B\left ( 6,0 \right )\,,\,C\left ( 4,4 \right ) such that P , Q , R are midpoints of sides BC , AC and AB .

We know that midpoint of line segment joining points \left ( x_1,y_1 \right )\,,\,\left ( x_2,y_2 \right ) is equal to \left ( \frac{x_1+x_2}{2}\,,\,\frac{y_1+y_2}{2} \right )

Midpoints P , Q , R :

P\left ( \frac{6+4}{2}\,,\,\frac{0+4}{2} \right )=P\left ( 5\,,\,2 \right )\\Q\left ( \frac{0+4}{2}\,,\,\frac{0+4}{2} \right )=Q\left ( 2\,,\,2 \right )\\R\left ( \frac{6+0}{2}\,,\,\frac{0+0}{2} \right )=R\left ( 3\,,\,0 \right )

We know that distance between points \left ( x_1,y_1 \right )\,,\,\left ( x_2,y_2 \right ) is given by \sqrt{\left ( x_2-x_1 \right )^2+\left ( y_2-y_1 \right )^2}

Length of AP :

AP = \sqrt{\left ( 5-0 \right )^2+\left ( 2-0\right )^2}=\sqrt{25+4}=\sqrt{29}

Length of BQ :

BQ = \sqrt{\left (2-6 \right )^2+\left ( 2-0 \right )^2}=\sqrt{16+4}=\sqrt{20}

Length of CR :

\sqrt{\left (3-4\right )^2+\left ( 0-4 \right )^2}=\sqrt{1+16}=\sqrt{17}

ANSWERED AT 16/02/2020 - 05:32 PM


QUESTION POSTED AT 16/02/2020 - 05:32 PM

Compute the following linear combinations. 4(-2,3)-2(6,-7) ...?

Answer:

Step-by-step explanation:

alright lets get started.

the linear combination is given by :

4(-2,3)-2(6,-7)

foiling 4 and 2 into the parenthesis

(4*-2, 4*3)+(-2*6,-2*-7)

(-8, 12)+(-12,14)

Combinig x and y terms together

(-8-12, 12+14)

(-20,26)    :     answer

Hope it will help. :)

ANSWERED AT 16/02/2020 - 05:32 PM


QUESTION POSTED AT 16/02/2020 - 05:32 PM

name the property used in each equation. then find the value of n. 2.) 1·n=8 3.) 28·n=0 4.) 0+n=22 5.) 1/4·n=1

2. n = 8 (Identity property)
3. n = 0 (Zero Property)
4. n = 22 (Additive Identity Property)
5. n = 4 (Fractal property)

ANSWERED AT 16/02/2020 - 05:29 PM


QUESTION POSTED AT 16/02/2020 - 05:29 PM

Consider the planes 2x + 1y + 5z = 1 and 2x + 5z = 0. (A) Find the unique point P on the y-axis which is on both planes. ( ? , ? , ? ) (B) Find a unit vector u with positive first coordinate that is parallel to both planes. ? I + ? J + ? K (C) Use the vectors found in parts (A) and (B) to find a vector equation for the line of intersection of the two planes,r(t) = ? I + ? J + ? K

B is easy, given 2x + 1y + 5z = 1 and 2x + 5z = 0, normal vectors of those planes are (2,1,5) and (2,0,5), cross product will give the parallel vector, divide by its length so it gives the unit vector

ANSWERED AT 16/02/2020 - 05:29 PM


QUESTION POSTED AT 16/02/2020 - 05:29 PM

Angle ABD and angle BDE are supplementary. Find the measures of both angles. m angle ABD =5x degrees, m angle BDE = (17x-18)degrees

By definition of supplementary angles,
∠ABD + ∠BDE = 180
5x + 17x - 18 = 180
22x = 198
x = 9

∠ABD = 5(9) = 45°
∠BDE = 180 - 45 = 135°

ANSWERED AT 16/02/2020 - 05:29 PM


QUESTION POSTED AT 16/02/2020 - 05:29 PM

Write the verbal sentence as an equation. Then solve the equation. 1.) negative sixteen plus the quotient of a number and 2 is 35. 2.) Thirty-nine minus a number is -19

1. -16 + x + 2= 35
x = 35 + 16
x = 51

2. 39 - x = -19
x = 39 + 19
x = 58

ANSWERED AT 16/02/2020 - 05:27 PM


QUESTION POSTED AT 16/02/2020 - 05:27 PM

Translate this word phrase into an equation. one increased by two equals the quotient of nine and three

Here is the equation for this word phrase:
1 + 2 = 9 / 3
Quotient is the result of division. 

ANSWERED AT 16/02/2020 - 05:26 PM


QUESTION POSTED AT 16/02/2020 - 05:26 PM

Suppose cos(π/2−x) =3/5, cos x =4/5 find sin, tan, csc, sec, cot

Cos (π/2 - x) = sin x = 3/5
tan x = sin x / cos x = 3/5 / 4/5 = 3/4
csc x = 1/sin x = 1 / 3/5 = 5/3
sec x = 1/cos x = 1 / 4/5 = 5/4
cot x = 1/tan x = 1 / 3/4 = 4/3.

ANSWERED AT 16/02/2020 - 05:26 PM


QUESTION POSTED AT 16/02/2020 - 05:26 PM

Find Dxy using the rules for finding derivatives. =(5x^2−8)(9x^2−3x+5)

You can do foil method first, to make it easier and to avoid product rule,
y= 45x^4 - 15x³ + 25x² - 72x² + 24x - 40
Simplify like terms,
y= 45x^4 - 15x³ - 47x² + 24x - 40
Now, find derivative,
dy/dx  = 180x³ - 45x² - 94x + 24 

ANSWERED AT 16/02/2020 - 05:13 PM


QUESTION POSTED AT 16/02/2020 - 05:13 PM

Simplify 12+3 [5+(4-2)]

Is the answer to your question 33

ANSWERED AT 16/02/2020 - 04:43 PM


QUESTION POSTED AT 16/02/2020 - 04:43 PM

How do i find the slope if i know it passes through two points??

Well you would use the equation y2-y1/x2-x1 to find any slope

ANSWERED AT 16/02/2020 - 04:36 PM


QUESTION POSTED AT 16/02/2020 - 04:36 PM

Work out the equation of this graph (picture included)

First, you have to identify what the graph is: a parabola, a circle, an ellipses, etc. it's a parabola.

to be totally honest, i don't know what the (1, 0) point is for. i thought it was meant to be the vertex, but it doesn't make sense? you find the vertex by calculating the midpoint, if nothing else, and the midpoint here is 0.5 ?? but i chose to disregard it and assume it to be a misprint

the graph gives you the x-intercepts, which are your "zeroes" -- this means that you can format them like so:

y = (x + 3)(x - 4)

this will give you your equation. you just have to list the zeroes as factors, then foil them to get a ax² + bx + c formula:

y = x² - x - 12

however, we generally prefer parabolas to be in vertex form. you can get it there by completing the square:

y = x² - x - 12
move the 12 so that it's with the y
y + 12 = x² - x

now you have to complete the square. this is done by taking your "middle" term on the right side, dividing it by 2, and squaring it:

(-1)/2 = -0.5
(-0.5)^2 = 0.25 or (1/4)

i'm going to write it as a decimal because it's easier to follow. when completing the square, whatever you add to one side, you must add to the other, so:

y + 12 + (0.25) = x² - x + (0.25)
then change the right side of the equation into a squared binomial
y + 12.25 = (x - 0.5)²
subtract 12.25 from each side
y = (x - 0.5)² - 12.25

y = (x - 0.5)² - 12.25 is your formula. 

ANSWERED AT 16/02/2020 - 04:26 PM


QUESTION POSTED AT 16/02/2020 - 04:26 PM

Solve x for the equations y=2x-10 2y=x-8

Hello,

Shall we begin?

y=2x-10 
2Y=x-8

2y= x - 8
2( 2x-10 ) = x - 8
4x - 20 = x - 8
4x - x = -8 + 20
3x = 12
x = 12/3
x = 4


Answers: x = 4

ANSWERED AT 16/02/2020 - 04:26 PM


QUESTION POSTED AT 16/02/2020 - 04:26 PM

A chemistry student needs to make 60 liters of a 30% alcohol solution. He has a 20% alcohol solution and a 40% alcohol solution in the lab. How many liters of each strength does he need to mix together *The system of equations I did was: a+b=60 & .2a+.4b=18. I may be wrong but i seriously need help

Hi i am sorry i am not sure what to do here i mainly answer questions in biology and maths so if u have any questions related to that subject u can ask me but chemsitry i am not really good at sorry xx

ANSWERED AT 16/02/2020 - 04:20 PM


QUESTION POSTED AT 16/02/2020 - 04:20 PM

If anyone can check my work for me that would be greatly appreciated I'm having trouble. Evaluate the expression foe the given value of the variable. |-4b-8|+|-1-b^2|+2b^3 ; b=-2 I got 1 for my answer -4(-2)-8-1+2^2+2(-2) 8-8-1+2^2-4 -1+2^2-4 1

The answer is -13. Solution: = |-4b - 8| + |-1 - b^2| + 2b^3 = |-4(-2) - 8| + |-1 - -2^2| + 2(-2)^3 = |8-8| + |-1+4| + 2(-8) = |0| + |3| + (-16) = -13

ANSWERED AT 16/02/2020 - 04:17 PM


QUESTION POSTED AT 16/02/2020 - 04:17 PM

The price of a gallon of unleaded gas was $2.89 yesterday. Today, the price fell to $2.82 . Find the percentage decrease. Round your answer to the nearest tenth of a percent

If u have $2.89 yesterday so you need to times $2.82 so I need th0 in the 10th percent so when u times 

ANSWERED AT 16/02/2020 - 04:11 PM


QUESTION POSTED AT 16/02/2020 - 04:11 PM

find a ratio equivalent to each ratio ` then use the ratios to write a proportion * 1) 22 / 30 2) 7 / 9 3) 18 / 54 4) 10 / 17

22/30 = 11/15
7/9 = 14/18
18/54 = 1/3
10/17 = 20/34

A proportion can be set up by using the general formula:
a/b = c/d
ad = bc

ANSWERED AT 16/02/2020 - 04:10 PM


QUESTION POSTED AT 16/02/2020 - 04:10 PM

Write the equation of the circle with center (-11, 3) and radius r = 9. Use the ^ key for the exponents. Write your answer as the example: (x - 4)^2+(y+8)^2=25

The equation of a circle with center (a, b) and radius = r is given by (x - a)^2 + (x - b)^2 = r^2
If center is (-11, 3) and radius is 9, then equation is
(x - (-11))^2 + (y - 3)^2 = 9^2
(x + 11)^2 + (y - 3)^2 = 81

ANSWERED AT 16/02/2020 - 04:09 PM


QUESTION POSTED AT 16/02/2020 - 04:09 PM