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

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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?
asked Feb 16, 2016 in PRECALCULUS by hana_24 Novice

1 Answer

+1 vote

The circle equation is image.

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

image

image

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

image

image.

Compare the equation with standard form of circle equation.

Here image

Therefore, the value of image is image.

answered Feb 16, 2016 by Sammi Mentor

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