Question

Assertion :Equation of an ellipse is of the form $3x^2+2y^2=6$, then its eccentricity '$e$' is $\frac{1}{\sqrt{2}}$. Reason: The eccentricity '$e$' of the ellipse is given by,
$e=\sqrt{1-\frac{a^2}{b^2}}$

• 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 D Assertion is incorrect but Reason is correct

Given equation is $3x^2+2y^2=6$

Here $a=\sqrt{2}$ and $b=\sqrt{3}$
Clearly, a < b, so the major and minor axes of the given ellipse are along $Y$ and $X$-axis respectively.
Length of the major axis $=2b=2\sqrt{3}$,
Length of the minor axis $=2a=2\sqrt{2}$
The coordinates of the vertices are $(0,\sqrt{3})$ and $(0,-\sqrt{3})$
$e=\sqrt{\frac{1}{3}}$