The equation of a circle is x² + y² - 8x + 9y + 15 = 0. Find its radius.

Correct Answer is : 12851/2{85}2185

Correct Answer is : 12851/2{85}2185

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WAEC Further Mathematics 2013 Paper

Question : 27

Total: 40

x^{2} + y^{2} - 8x + 9y + 15 = 0

. Find its radius.

Solution:

Concept:

The standard form of a circle is

(x-a)^2 + (y-b)^2 = r^2

Comparing with the given equation helps find the radius

r

Explanation:

Given:

x^2 + y^2 - 8x + 9y + 15 = 0

Rearrange:

(x^2 - 8x) + (y^2 + 9y) = -15

Complete the square for

x

x^2 - 8x + 16 = (x-4)^2

Complete the square for

y

y^2 + 9y + \frac{81}{4} = \left(y + \frac{9}{2}\right)^2

Add these constants to both sides:

(x-4)^2 + \left(y+\frac{9}{2}\right)^2 = -15 + 16 + \frac{81}{4}

Simplify the right side:

-15 + 16 + \frac{81}{4} = 1 + \frac{81}{4} = \frac{85}{4}

Hence,

r^2 = \frac{85}{4}

Taking the positive square root:

r = \sqrt{\frac{85}{4}} = \frac{1}{2}\sqrt{85}

Answer:

The radius is

\frac{1}{2}\sqrt{85}

, which is option C.

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