Question

A circle in the xy-coordinate plane has the equation x2 + y2 +6y -4 = 0. If the equation of the circle is written in the form x2 + (y+k)2 = c.

where k and care constants, what is the value of K?

Answer 1

k = 3

Explanation:

Given

x² + y² + 6y - 4 = 0 ( add 4 to both sides )

x² + y² + 6y = 4

Using the method of completing the square

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

x² + y² + 2(3)y + 9 = 4 + 9

x² + (y + 3)² = 13

with k = 3