Question

What is the center of a circle represented by the equation (x−5)2 (y 6)2=42? (−6,5) (−5,6) (5,−6) (6,−5).

Answer 1

The center of the circle is (5, -6). Option C shows the center of the circle.

What is a circle?

A circle can be defined as the set of all points in the plane that are a fixed distance from a fixed point on the plane.

Given that the equation of the circle is,

$(x-5)^2+(y+6)^2=42$

We know that the general form of the equation of the circle is,

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

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

Compare the given equation with the general form of the equation, we get,

$(x-h) = (x-5)$ and $(y-k) = (y+6)$ and $r^2 = 42$

For x-axis,

$(x-h) =(x-5)$

$h = 5$

For y-axis,

$(y-k) = (y+6)$

$k = -6$

Hence we can conclude that the center of the circle is (5, -6). Option C shows the center of the circle.

To know more about the equation of the circle, follow the link given below.

https://brainly.com/question/10165274.