Question

Assertion :Ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ and $12x^2-4y^2=27$ intersect each other at right angle. Reason: Whenever confocal ellipse & hyperbola intersect, they intersect each other orthogonally.

• 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 A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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

Focus $(ae,0)=(3,0)$

and $12x^2-4y^2=27$

Focus $(ae,0)=(3,0)$

Since, ellipse and hyperbola are confocal they intersect orthogonally.