Question

Assertion :From a point $(\alpha ,5)$, tangents are drawn to $\frac{x^2}{25}+\frac{y^2}{16}=1$ and are $\perp$ to each other, then $\alpha =\pm 4$. Reason: The locus of point of intersection of $\perp$ tangents to $\frac{x^2}{25}+\frac{y^2}{16}=1$ is $x^2+5y=41$.

• 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. Both Assertion and Reason are incorrect

Answer 1

The correct option is C Assertion is correct but Reason is incorrect

The locus of the $\perp$ tangents to an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is director circle whose equation is $x^2+y^2=a^2+b^2$
Now $(\alpha ,5)$ lies on $x^2+y^2=25+16\Rightarrow {\alpha }^2+25=25+16\Rightarrow \alpha =\pm 4$
As Assertion (A) is true but Reason (R) is false.