Question

Find the equation for the circle with center (1,3) and passing through (-2,-1). Write the equation for the circle.

Answer 1

(x-1)^2 + (y-3)^2 = 25

Explanation:

d = square root [(-2-2)^2 + (-1-3)^2] =

square root (-3^2 + 4^2)

= square root 25

Radius = 5

Answer 2

`(x - 1)^(2) + (y - 3)^(2) = 25`

Explanation:

Remember that a circle's equation is defined as
`(x - h)^(2) + (y - k)^(2) = r^(2)`, where (h, k) defines the center ["h" is the number of units shifted right, "y" is the number of units shifted up], and "r^2" is the radius squared.

We already know the center is (1, 3), so we already know the "h" and "k" values:
`(x - 1)^(2) + (y - 3)^(2) = r^(2)`

Now, simply plug in the value that the circle passes through to find "r^2":

`(-2 - 1)^(2) + (-1 - 3)^(2) = r^(2)\\(-3)^(2) + (-4)^(2) = r^(2)\\9 + 16 = r^(2)\\25 = r^(2)`

Finally, plug in our known values for h, k, and r^2:

`(x - 1)^(2) + (y - 3)^(2) = 25`

This is our equation.