If $2 x^{2} + 2 y^{2} - 12 x + 8 y + k = 0$ is a point circle, then the value of $k$ is

18

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12

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13

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26

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Solution

The correct option is D $26$
Given equation of circle is $2 x^{2} + 2 y^{2} - 12 x + 8 y + k = 0$
The equation can be rewritten as,
$x^{2} + y^{2} - 6 x + 4 y + \frac{k}{2} = 0$
Comparing it with general form of circle,
$g = - 3, f = 2, c = \frac{k}{2}$

We know that, the radius of the point circle is $0$ , so
$r = \sqrt{g^{2} + f^{2} - c} = 0 \Rightarrow g^{2} + f^{2} - c = 0 \Rightarrow (- 3)^{2} + (2)^{2} - \frac{k}{2} = 0 ∴ k = 26$

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