Question

The center of a circle represented by the equation (x + 9)2 + (y − 6)2 = 102 is .

Answer 1

Answer:

The center of the circle is (-9,6).

Step-by-step explanation:

The given equation is

$(x+9)^2+(y-6)^2=102$

The standard form of the circle is

$(x-h)^2+(y-k)^2=r^2$    .... (1)

Where (h,k) is the center of the circle and r is the radius of the circle.

The given equation can be rewritten as

$(x-(-9))^2+(y-6)^2=(\sqrt{102})^2$  .... (2)

On comparing (1) and (2), we get

$h=-9$

$k=6$

$r=\sqrt{102}$

Therefore the center of the circle is (-9,6) and the radius is $\sqrt{102}$.

Answer 2

The center of the circle (x + 9)² + (y − 6)² = 102 is (h, k) is calculated as (-9, 6).

What is the circle?

It is a special kind of ellipse whose eccentricity is zero and foci are coincident with each other. It is a locus of a point drawn at an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.

Given

The equation of circle is (x + 9)² + (y − 6)² = 102

To find

The center of the circle.

How to find the center of the circle?

We know the standard equation of the circle,

(x - h)² + (y − k)² = r²

Compare the equations, we get

-h = 9 then h = -9.

- k = - 6 then k = 6

Hence, the center of the circle is (-9, 6).

More about the circle link is given below.
https://brainly.com/question/11833983