Question

Assertion :If the equation of a hyperbola is $3x^2-6y^2=-18$, then length of its latus rectum is $4\sqrt{3}$ Reason: Length of latus rectum of a hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=-1$ is $\frac{2a^2}{b}$

• 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 equation is $3x^2-6y^2=-18$

Dividing both sides by $-18$, we get
$\frac{-x^2}{6}+\frac{y^2}{3}=1$
$a=-\sqrt{6},b=\sqrt{3}$
Therefore, latus rectum $\frac{2a^2}{b}=\frac{2(-\sqrt{6}{)}^2}{\sqrt{3}}$

$=\frac{12}{\sqrt{3}}$

$=4\sqrt{3}$