Question

Assertion (A): Equation of the normal to the ellipse $\frac{x^2}{25}+\frac{y^2}{9}=1$ at $P(\frac{\pi }{4})$ is $5x-3y-8\sqrt{2}=0$
Reason (R): Equation of the normal to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ at $P(x_1,y_1)$ is $\frac{a^{2}x}{x_1}-\frac{b^{2}y}{y_1}=a^2-b^2$

• A. Both A and R are true but R is not the correct explanation of A
• B. Both A and R are true and R is the correct explanation of A
• C. A is true but R is false
• D. A is false but R is True

Answer 1

Answer: (B)

Both A and R are true and R is the correct explanation of A

Reason is correct.
Equation of normal in parametric form: $\frac{ax}{\cos \theta }-\frac{by}{\sin \theta }=a^2-b^2$
$\Rightarrow 5\sqrt{2}x-3\sqrt{2}y=25-9=16$
Therefore, assertion is correct but reason is not the correct explanation