Question

prove that 3x square +3y square - 6x + 4y -1 =0 , represent a circle . find its centre and radius​

Answer 1

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Answer 2

Center=$(1,-\frac{2}{3})$

Radius,r$=\frac{4}{3}$ units

Step-by-step explanation:

$3x^2+3y^2-6x+4y-1=0$

Divide by 3 on both sides of equation

$x^2+y^2-2x+\frac{4}{3}-\frac{1}{3}=0$

The general equation of circle  is given by

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

Where Center=(-g,-f)

Radius,$r=\sqrt{g^2+f^2-c}$

It is in the form of equation circle.

Hence, the equation represents the equation of circle.

By comparing we get

g=-1 and f=$\frac{2}{3}$

Center=(-g,-f)=$(1,-\frac{2}{3})$

c=$-\frac{1}{3}$

Radius,r=$\sqrt{(-1)^2+(\frac{2}{3})^2+\frac{1}{3}}=\frac{4}{3}$ units

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