Question

Write the following equation in standard form and show your work : x^2+y^2-22y+96=0

Answer 1

`x^2 + (y-11)^2 = 5`

Explanation:

Completing the square gives us that

`x^2+y^2-22y+96=0\\x^2 + (y-11)^2 - 11^2 + 96 = 0\\x^2 + (y-11)^2 = 121 - 96\\x^2 + (y-11)^2 = 25\\x^2 + (y-11)^2 = 5`

Which is the standard form of a circle.