Number of tangents to $y^{2} = 2 x$ through $(1, 2)$ is

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Solution

The correct option is C $2$
Let $S = y^{2} - 2 x$
$∴ S_{(1, 2)} = 2 > 0$
Hence the given point lies outside of the parabola
So, $2$ tangents can be drawn from any point which lies outside.

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