First slide

Parabola

Question

$The equation of the common tangent to the curves y^{2} = 8 x and x y = - 1, is$

Moderate

A

$3 y = 9 x + 2$
B

$y = 2 x + 1$
C

$2 y = x + 8$
D

$y = x + 2$

Solution

$\begin{array}{l} General equation of tangent to the curve \\ y^{2} = 8 x is y = m x + \frac{2}{m} - - - - - - (1) \end{array}$
$Now on solving it with xy = - 1$
$x (m x + \frac{2}{m}) = - 1 m^{2} x^{2} + 2 x + m = 0 put discriminant = 0 4 - 4 m^{3} = 0 \Rightarrow m = 1$
sub in(1) y=x+2

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