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Using the following equation, find the center and radius of the circle. You must show and explain all work and calculations to receive credit. Be sure to leave your answer in exact form.
x^2 + y^2 - 8x + 2y + 13 = 0

Sagot :

Answer:

Step-by-step explanation:

x²-8x+16+y²+2y+1=16+1-13
(x-4)²+(y+1)²=2²


general form of a circle's equation is
(x-h)^2 + (y-k)^2 = r^2
Where (h,k) is the center and r= radius
By comparing with A,
(4,-1) is center and radius= 2.

MrRoyalidn

The center of the circle is (-4,2) and the radius is 2

How to determine the center and the radius?

The equation is given as:

x^2 + y^2 - 8x + 2y + 13 = 0

Rewrite as:

x^2 - 8x + y^2  + 2y + 13 = 0

Subtract 12 from both sides

x^2 - 8x + y^2  + 2y = -13

Group each variable

[x^2 - 8x] + [y^2  + 2y] = -13

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Take the coefficient of x and y

-8 and 2

Divide by 2

-4 and 1

Square both numbers

16 and 1

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Next, we add 16 and 1 to both sides of the equation

[x^2 - 8x + 16] + [y^2  + 2y + 1] = -13 + 16 + 1

Express as perfect squares and evaluate the sum

(x - 4)^2 + (y + 1)^2 = 4

Express 4 as 2^2

(x - 4)^2 + (y + 1)^2 = 2^2

A circle is represented as:

(x - a)^2 + (y - b)^2 = r^2

Where:

Center = (a,b)

Radius = r

This means that the center of the circle is (-4,2) and the radius is 2

Read more about circle equation at:

https://brainly.com/question/1559324

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