Question

Assertion :If the equation of the ellipse is given to be $16x^2+25y^2=400$, then length of the major axis is $10$. Reason: Length of the major axis $=$ $2b$

• 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 C Assertion is correct but Reason is incorrect

We have, $16x^2+25y^2=400$

$\Rightarrow \frac{16x^2}{400}+\frac{25y^2}{400}=1$

$\Rightarrow \frac{x^2}{25}+\frac{y^2}{16}=1$,
where $a^2=25$ and $b^2=16$
i.e. $a=5$ and $b=4$.
Clearly, $a>b$, therefore, the major and minor axes of the ellipse are along $x$ and $y$ axes respectively.
Hence, length of major axis $=$ $2a$ $=$ $10$.