Question

How do you write the general form of a circle given center is (4,-6) and tangent to line x=-1?

Answer 1

`(x -4)^2 +(y+6)^2 = 25`

Explanation:

The general form of a circle is `(x - h)^2 + (y-k)^2 = r^2` where `(h,k)` is the center of the circle and `r` is the radius.

the radius can be calculated as the distance from the center to the tangent line, which is given by the difference in their x-coordinates.
`r = 4- (-1) = 5`

The general equation is therefore

`(x -4)^2 +(y+6)^2 = 25`