Question

How do you write the general form of a circle given characteristics. Center: (−5, 1); solution point: (0, 0)?

Answer 1

`(x + 5)^2 + (y-1)^2 = 26`

Explanation:

A circle of radius `r`, centered at `(h, k)` has the form

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

From the given information, we have `h = -5` and `k = 1`. To find `r`, we need only find the distance from the center `(h, k)` to a point on the circle. As `(0, 0)` is such a point, applying the distance formula gives us

`r = sqrt((-5-0)^2 + (1-0)^2) = sqrt(26)`

Thus the desired equation is

`(x-(-5))^2 + (y - 1)^2 = sqrt(26)^2`

or, simplifying,

`(x + 5)^2 + (y-1)^2 = 26`