Parabola 2 Question 8

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

(2014 Main)

(a) $\frac{1}{2}$

(b) $\frac{3}{2}$

(c) $\frac{1}{8}$

(d) $\frac{2}{3}$

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Answer:

Correct Answer: 8. (b)

Solution:

  1. Let the tangent to parabola be $y=m x+a / m$, 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 $\quad x^{2}=-32 y$

$\therefore \quad x^{2}=-32 m x+\frac{1}{m}$

$\Rightarrow \quad x^{2}+32 m x+\frac{32}{m}=0$

$$ D=0 $$

$\because \quad(32 m)^{2}-4 \cdot \frac{32}{m}=0 \quad \Rightarrow \quad m^{3}=1 / 8$

$\therefore \quad m=1 / 2$



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