Find the coordinates of the centre of the circle 3x²+3y² - 4x + 8y -2=0

Correct Answer is : ( 23, −43\;2/3, \;-4/332,3−4)

Correct Answer is : ( 23, −43\;2/3, \;-4/332,3−4)

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WAEC Further Mathematics 2017 Paper

Question : 5

Total: 40

3x^{2}+3y^{2} - 4x + 8y -2=0

Solution:

Concept:

For a circle

x^2 + y^2 + 2gx + 2fy + c = 0

, the centre is

(-g, -f)

Explanation:

Divide the given equation by

3

x^2 + y^2 - \frac{4}{3}x + \frac{8}{3}y - \frac{2}{3} = 0

Compare this with

x^2 + y^2 + 2gx + 2fy + c = 0

Here,

2g = -\frac{4}{3}

and

2f = \frac{8}{3}

So,

g = -\frac{2}{3}

and

f = \frac{4}{3}

Therefore, the centre is

(-g, -f) = \left(\frac{2}{3}, -\frac{4}{3}\right)

Answer:

Option C:

\left(\frac{2}{3}, -\frac{4}{3}\right)

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