SATHEE: Application of Derivatives 1 Question 7

Application of Derivatives 1 Question 7

####7. If the curves $y^{2} = 6 x, 9 x^{2} + b y^{2} = 16$ intersect each other at right angles, then the value of $b$ is

(2018 Main)

(a) 6

(b) $\frac{7}{2}$

(d) $\frac{9}{2}$

Show Answer

Answer:

Correct Answer: 7. (b, d)

Solution:

We have, $y^{2} = 6 x$

$\Rightarrow 2 y \frac{d y}{d x} = 6 \Rightarrow \frac{d y}{d x} = \frac{3}{y}$

Slope of tangent at $(x_{1}, y_{1})$ is $m_{1} = \frac{3}{y_{1}}$

Also, $9 x^{2} + b y^{2} = 16$

$\Rightarrow 18 x + 2 b y \frac{d y}{d x} = 0 \Rightarrow \frac{d y}{d x} = \frac{- 9 x}{b y}$

Slope of tangent at $(x_{1}, y_{1})$ is $m_{2} = \frac{- 9 x_{1}}{b y_{1}}$

Since, these are intersection at right angle.

$\begin{aligned} ∴ & m_{1} m_{2} = - 1 \Rightarrow & \frac{27 x_{1}}{b y_{1}^{2}} & = 1 \\ \Rightarrow & \frac{27 x_{1}}{6 b x_{1}} & = 1 \\ \Rightarrow & b & = \frac{9}{2} & [∵ y_{1}^{2} = 6 x_{1}] \end{aligned}$

Application of Derivatives 1 Question 7

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Application of Derivatives 1 Question 7

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Menu