Equation of common tangents to parabola {y^2} = 8x and hyperbola 3{x^2} - {y^2} = 3 , is

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10-2. Parabola, Ellipse, Hyperbola

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The equation of common tangents to the parabola ${y^2} = 8x$ and hyperbola $3{x^2} - {y^2} = 3$, is

A

$2x \pm y + 1 = 0$

B

$2x \pm y - 1 = 0$

C

$x \pm 2y + 1 = 0$

D

$x \pm 2y - 1 = 0$

Solution

(a) Tangent to ${y^2} = 8x$

==> $y = mx + \frac{2}{m}$

Tangent to $\frac{{{x^2}}}{1} – \frac{{{y^2}}}{3} = 1$

==> $y = mx \pm \sqrt {{m^2} – 3} $

On comparing, we get

m = $\pm$ $2$ or tangent as $2x \pm y + 1 = 0$.

Standard 11

Mathematics

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