Question

Apex help asap

The circle given by x^2 + y^2 - 2y - 11y = 0 can be written in standard form like this: x^2 + (y-k)^2 = 12

What is the value of k in this equation?

Answer 1

k = 1

Explanation:

Given

x² + y² - 2y - 11 = 0 ( add 11 to both sides )

x² + y² - 2y = 11

To express in standard form use the method of completing the square on

y² - 2y

To complete the square

add ( half the coefficient of the y- term )² to both sides

x² + y² + 2(- 1)y + 1 = 11 + 1

x² + (y - 1)² = 12 ← as required

with k = 1