The slope of the line touching both the parabolas y2 = 4x and x2 =

Engineering

Mathematics

Tangent of Parabola

Question

The slope of the line touching both the parabolas y² = 4x and x² = – 32y is

$\frac{1}{8}$

$\frac{1}{2}$

$\frac{2}{3}$

$\frac{3}{2}$

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y = mx + $\frac{1}{m}$ is tangent to parabola x² = – 32y also

$∴ x^{2} = - 32 (mx + \frac{1}{m})$

$x^{2} + 32mx + \frac{32}{mk} = 0$

its $∆$ = 0 gives m = $\frac{1}{2}$