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WAEC Further Mathematics 2012 Paper

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Question : 10

Total: 40

The equation of a circle is

3x^{2} + 3y^{2} + 24x - 12y = 15

. Find its radius.

2
3
4
5

Solution:

Concept:

Convert the given circle equation into the standard form

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

.

Explanation:

Divide the whole equation by

3

.

We get

x^2 + y^2 + 8x - 4y = 5

.

Compare with

x^2 + y^2 - 2ax - 2by = r^2 - a^2 - b^2

.

Here,

-2a = 8

, so

a = -4

.

Also,

-2b = -4

, so

b = 2

.

Now use

r^2 - a^2 - b^2 = 5

.

So

r^2 = 5 + a^2 + b^2 = 5 + 16 + 4 = 25

.

Therefore,

r = \sqrt{25} = 5

.

Answer:

Radius

= 5

, which is option D.

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