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:
- 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 $\quad x^{2}=-32 y$
$\therefore \quad x^{2}=-32 m x+\frac{1}{m}$
$\Rightarrow \quad x^{2}+32 m x+\frac{32}{m}=0$
$$ D=0 $$
$\because \quad(32 m)^{2}-4 \cdot \frac{32}{m}=0 \quad \Rightarrow \quad m^{3}=1 / 8$
$\therefore \quad m=1 / 2$
