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Question
Show that the equation 3x2 + 3y2 + 12x + 18y − 11 = 0 represents a circle
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Solution
Given equation is
3x2 + 3y2 + 12x + 18y − 11 = 0
Dividing throughout by 3, we get
`x^2 + y^2 + 4x + 6y - 11/3` = 0
Comparing this equation with
x2 + y2 + 2gx + 2fy + c = 0, we get
2g = 4, 2f = 6, c = `-11/3`
∴ g = 2, f = 3, c = `-11/3`
Now, g2 + f2 – c = `(2)^2 + (3)^2 - (-11/3)`
= `4 + 9 + 11/3`
= `50/3 > 0`
∴ The given equation represents a circle.
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