SATHEE: Parabola 2 Question 29

Parabola 2 Question 29

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) $\frac{3}{2}$

(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 $x^{2} = - 32 y$

$∴ x^{2} = - 32 m x + \frac{1}{m}$

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

$D = 0$

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

$∴ m = 1 / 2$

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Parabola 2 Question 29

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

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