Question

Assertion :$\frac{1}{r}-\frac{3}{5}=\frac{3\cos \theta }{5}$ represents a parabola Reason: A conic is said to be a parabola if its eccentricity is $1$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Given conic is, $\frac{1}{r}-\frac{3}{5}=\frac{3cos\theta }{5}$
$\Rightarrow \frac{1}{r}=\frac{3}{5}+\frac{3\cos \theta }{5}$
$\Rightarrow \frac{5/3}{r}=1+\cos \theta$
Comparing it with equation of general conic, $\frac{l}{r}=1+e\cos \theta$
$\Rightarrow e=1\therefore$ given conic is parabola.