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Principal Axes of Ellipse

Find the valu...

Question

Find the value of $c$ if $(2, 3)$ lie on the circle $x^{2} + y^{2} + 2 x + 3 y + c = 0$

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Solution

The equation of circle is $x^{2} + y^{2} + 2 x + 3 y + c = 0$
It passes through $(2, 3)$
$⟹ 2^{2} + 3^{2} + 2 (2) + 3 (3) + c = 0 4 + 9 + 4 + 9 + c = 0 c = - 26$

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