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Definition of Circle

The equation ...

Question

The equation of the circle passing through $(3, 6)$ and whose centre is $(2, - 1)$ is

x^{2} + y^{2} - 4 x + 2 y = 45

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x^{2} + y^{2} - 2 y + 45 = 0

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x^{2} + y^{2} + 4 x - 2 y = 45

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x^{2} + y^{2} + 2 y + 45 = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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Solution

The correct option is A $x^{2} + y^{2} - 4 x + 2 y = 45$
Let the equation be $x^{2} + y^{2} + f x + g y + d = 0$ with centre = $(- \frac{- f}{2}, - \frac{g}{2})$
Hence, $f = - 4, g = 2$
Equation becomes = $x^{2} + y^{2} - 4 x + 2 y + d = 0$
Putting x = 3 y = 6 in the above equation we get
$9 + 36 - 12 + 12 + d = 0$
$⟹ d = - 45$
$e q u a t i o n = x^{2} + y^{2} - 4 x + 2 y - 45 = 0$

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