Question

Can someone tell me how to do this problem? please

Answer 1

Hi there, here's your answer:

The general formula of a circle:

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

Where the ordered pair (h, k) is the center of the circle.

Given (h, k) = (-6, -2)

We also have that the circle passes through a point (7, 12)

Which means that (7, 12) lies on the circumference of the circle.

Let this be labelled as
`(x_(1), y_(1))`

Since this point lies on the circumference of the circle, it must satisfy the equation when substituted in for (x, y).

Thus, we substitute
`x_(1)` for x and
`y_(1)` for y.

We get the final equation to be:

`(7+6)^2 + (12+2)^2 = r^2`

Or

`169 + 196 = r^2`

`r^2 = 365`

Thus, we get the final equation of the circle to be
`(x+6)^2 + (y+2)^2 = 365`

Hope it helps!