Question

Assertion :Tangents drawn from any point on the circle $x^2+y^2=225$ to the ellipse $\frac{x^2}{144}+\frac{y^2}{81}=1$ are at right angle. Reason: Equation of the auxiliary circle of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is $x^2+y^2=a^2$.

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

As $x^2+y^2=225$ is the director circle of the ellipse $\frac{x^2}{144}+\frac{y^2}{81}=1$ and tangents drawn from any point on the director circle to the given ellipse are at right angle.
So, statement-1 is true.
Statement -2 is also true. But, it is not an explanation for statement -1.