Question

A circle given by the x^2 + y^2 -2y -11 = 0, what is the value of K?

A circle given by

x^2 + y^2 -2y -11 = 0

can be written in standard form like this

x^2 + ( y - k)^2 = 12

What is the value of k in this eqation?

Answer 1

The circle equation is .

The standard form of circle equation is , where is center of circle and is radius of circle.

To change the expression into a perfect square trinomial add (half the y coefficient)² to each side of the expression.

.

Compare the equation with standard form of circle equation.

Here

Therefore, the value of is .