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Slope Form of Tangent: Hyperbola

The equation ...

Question

The equation of the common tangents to $x^{2} + 4 y^{2} = 8$ and $y^{2} = 4 x$ can be

A

2 x + y - 4 = 0

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B

2 x - y + 4 = 0

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C

x - 2 y + 4 = 0

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D

x + 2 y + 4 = 0

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Solution

The correct option is D $x + 2 y + 4 = 0$
Let the tangent be $y = m x + \frac{1}{m}$
$x^{2} + 4 {(m x + \frac{1}{m})}^{2} = 8$ has equal roots
$\Rightarrow m = - \frac{1}{2}, m = \frac{1}{2}$

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Slope Form of Tangent: Hyperbola

Standard XII Mathematics

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