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  • The slope of the line touching both the parabolas <img alt="y^2=4 x \text { and } x^2=-32 y" src="https://entrancecorner.oncodecogs.com/gif.latex?y%5E2%3D4%20x%20%5Ctext%20%7B%20and%20%7D

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

Option: 1

\begin{aligned} & \frac{1}{2} \\ \end{aligned}


Option: 2

\frac{3}{2} \\


Option: 3

\frac{1}{8} \\


Option: 4

\frac{1}{8}


Answers (1)

best_answer

Let tangent to the parabola be  y=m x+\frac{a}{m}  .If it touches the other curve, then D = 0, to get the value of m.

For parabola,y^2=4 x

Let y=m x+\frac{1}{m}  be tangent line and it touches the parabola x^2=-32 y

\begin{aligned} \therefore & x^2=-32\left(m x+\frac{1}{m}\right) \\ & \Rightarrow x^2+32 m x+\frac{32}{m}=0 \\ D & =0 \\ \because & (32 m)^2-4 \cdot\left(\frac{32}{m}\right)=0 \\ \Rightarrow & m^3=\frac{1}{8} \\ \therefore & m=\frac{1}{2} \end{aligned}

Posted by

Sanket Gandhi

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