Question

Assertion :Tangents drawn from any point on the circle $x^2+y^2=13$ to the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$ are at right angles. Reason: Equation of the auxilliary circle of the ellipse $\frac{x^2}{13}+\frac{y^2}{4}=1$ is $x^2+y^2=13$

• 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 B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

Statement-1 is true as $x^2+y^2=9+4$ is the equation of the director circle of the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$, which is the locus of the point of intersection of the tangents to the ellipse which are at right angles.

Statement-2 is also true as $x^2+y^2=13$ is the circle on the major axis of the ellipse as diameter and hence by definition is the auxiliary circle but Statement-1 does not follow from Statement-2.
Ans: B