Question

What is the equation of the circle?

Answer 1

Step-by-step explanation:

The equation of a circle is

`(x - h) {}^(2) + (y - k) {}^(2) = {r}^(2)`

Where (h,k) is the center and

r is the radius.

Here the center is (-9,10).

To find the radius, find the distance from the center to a point on the circle.

So find the distance between (-9,10) and (-9,7).

`r = \sqrt{(( - 9 - ( - 9) {}^(2) + (10 - 7) {}^(2) }`

`r = √(0 + 9)`

`r = √(9)`

`r = 3`

So the radius is 3 so we plug in

`(x - ( - 9) {}^(2) + (y - 10) {}^(2) = {3}^(2)`

`(x + 9) {}^(2) + (y - 10) {}^(2) = 9`

Answer 2

○
`\displaystyle (x + 9)^2 + (y - 10)^2 = 9`

Step-by-step explanation:

Accourding to one of the circle equations,
`\displaystyle (x - h)^2 + (y - k)^2 = r^2,`the centre of the circle is represented by
`\displaystyle (h, k).`Moreover, all negative symbols give you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must pay cloce attention to which term gets which symbol. Another thing you need to know is that the radius will ALWAYS be squared, so no matter how your equation comes about, make sure that the radius is squared.

I am joyous to assist you at any time.