Question

Write a quadratic equation to represent the circle graphed on the right

Answer 1

The standard form: x² + (y + 1)² = 25

The general form: x² + y² + 2y - 24 = 0

Explanation:

The equation of a circle:

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

(h, k) - center

r - radius

We have the center (0, -1) and the radius r = 5 (look at the picture).

Substitute:

`(x-0)^2+(y-(-1))^2=5^2\\\\x^2+(y+1)^2=25`

use (a + b)² = a² + 2ab + b²

`x^2+y^2+2y+1=25` subtract 25 from both sides

`x^2+y^2+2y-24=0`