piperfurford
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A circle is defined by the equation x2 + y2 + 8x + 22y + 37 = 0. What are the coordinates for the center of the circle and the length of the radius?

Respuesta :

gwpc40
We can say that:
8x = -2ax
8 = -2a
a = -4

22y = - 2by
22 = -2b
b = -11

37 = a² + b² - r²
37 = (-4)² + (-11)² - r²
r² = 16 + 121 - 37
r² = 100
r = 10

With all this information, we can say that:
The center of the circle is: (-4 ; -11)
and the radius of the circle is r = 10

P.S:
(a - x)² + (b-y)² = r²
a² - 2ax + x² + b² -2by + y² - r² = 0
x² + y² -2ax - 2by + a² + b² - r² = 0

The center of the circle is: (-4 ; -11) and the radius of the circle is r = 10

What is equation of circle?

The general equation for a circle is (x-a)² + (y-b)² = r², where ( a, b ) is the center and r is the radius.

Given:

x² + y² + 8x + 22y + 37 = 0.

Now, to find both coordinates and radius write the given equation in standard form:

(x-a)² + (y-b)² = r²

x² + 8x +  y²+ 22y= -37

( x² + 2* x*4 + 4²)+(  y² + 2*y* 11 + 11²) = -37 + 16 + 121

(x + 4)² + ( y+ 11)² = 100

(x + 4)² + ( y+ 11)² = 10²

So, center of the circle is: (-4 ; -11)

and the radius of the circle is r = 10

Learn more about this concept here;

https://brainly.com/question/16505663

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