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Question
Find centre and radius of the following circles
2x2 + 2y2 – 6x + 4y + 2 = 0
Solution
2x2 + 2y2 – 6x + 4y + 2 = 0
(÷ by 2) ⇒ x2 + y2 – 3x + 2y + 1 =0
Comparing this equation with the general form of the circle we get
2g = – 3
2f= 2
g = `- 3/2`
g = 1
c = 1
So centre = (– g, – f) = `(3/2, -1)`
And radius = `sqrt(g^2 + f^2 - "c")`
= `sqrt(9/4 + 1 - 1)`
= `3/2`
∴ Centre = `(3/2, -1)` and radius = `3/2`
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