Question

The slope of the line touching both the parabolas y^2=4x and x^2=-32y is

Answer 1

Answer:

The slope of the line touching both the parabolas y^2=4x and x^2=-32y is

Step-by-step explanation:

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Answer 2

$\large\underline\mathrm\red{Solution}$

• Let the tangent to parabola be y = Mx + a/m, if it touches the other curve, then D = 0, to get the value of m.

$\large\mathrm\red{For \: parabola}$, y² = 4x

Let y = mx + 1/m be tangent line and it touches the parabola.

x² = -32y

x² = -32( Mx + 1/m )

x² + 32mx + 32/m = 0

$\large\underline\mathrm\red{D = 0}$

(32m)² - 4.(32/m) = 0

m³ = 1/8

m = 1/2

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