Question

Rewrite the equation of the circle in vertex form.
x2 + y2 - 2y - 15 - 0

Answer 1

`\underline{\,\bold{x^2+(y-1)^2=16}\,}`

Explanation:

`x^2 + y^2 - 2y - 15 = 0\\\\ \underbrace{x^2 + 2\cdot x\cdot0 +0^2} + \underbrace{y^2 - 2\cdot y\cdot1 + 1^2}-1^2 - 15 = 0\\\\{}\qquad\ \ (x+0)^2\quad\ +\ \quad(y-1)^2\quad\ -\quad16=0\\\\x^2+(y-1)^2=16`