Question

Find an equation of the circle that has center (0, 4) and passes
through (6, 6).

Answer 1

`{x}^(2) + {y}^(2) - 8y - 24 = 0`

Answer 2

x² +(y -4)² = 40

Explanation:

You want the equation of the circle centered at (0, 4) through point (6, 6).

Equation

The standard form equation of a circle centered at (h, k) through points (x, y) is ...

(x -h)² +(y -k)² = r²

where r is the radius of the circle.

We can find the value of r² using the given center and point. For (x, y) = (6, 6) and (h, k) = (0, 4), we have ...

(6 -0)² +(6 -4)² = r² = 36 +4 = 40j

Then for (h, k) = (0, 4) and r² = 40, we have the equation of the circle as ...

x² +(y -4)² = 40