# Get Answers to all your Questions

### Answers (1)

Answer:

$\frac{-b}{a^{2}y^{3}}$

Hint:

You must know about derivative of second order

Given:

\begin{aligned} &{\text { If } x}=a \cos \theta, y=b \sin \theta \\ &\text { Show that } \frac{d^{2} y}{d x^{2}}=\frac{-b}{a^{2} y^{3}} \end{aligned}

Solution:

\begin{aligned} &{\text {Let}\: \: x}=a \cos \theta, y=b \sin \theta \\ \end{aligned}

\begin{aligned} &\frac{d y}{d x}=\frac{\frac{d y}{d \theta}}{\frac{d x}{d \theta}} \\ &\frac{d^{2} y}{d x^{2}}=\frac{\frac{d}{d \theta}\left(\frac{d y}{d x}\right)}{\frac{d x}{d \theta}} \\ &x=a \cos \theta, y=b \sin \theta \\ &\frac{d x}{d \theta}=-a \sin \theta \frac{d y}{d \theta}=b \cos \theta \\ &\frac{d y}{d x}=\frac{-b}{a} \cot \theta \end{aligned}

\begin{aligned} &\frac{\frac{\mathrm{d} }{\mathrm{d} \theta }(\frac{dy}{dx})}{\frac{dx} {d\theta }}=\frac{\frac{b}{a} \cos e c^{2} \theta}{-a \sin \theta} \quad\left(\frac{d}{d \theta} \cot \theta=\cos e c^{2} \theta\right) \\ &\frac{-b \times b^{3}}{a^{2} \sin ^{3} \theta \times b^{3}} \\ &\frac{d^{2} y}{d x^{2}}=\frac{-b}{a^{2} y^{3}} \end{aligned}

Hence proved

View full answer

## Crack CUET with india's "Best Teachers"

• HD Video Lectures
• Unlimited Mock Tests
• Faculty Support