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Statement-1: Tangents drawn from any poi...

Statement-1: Tangents drawn from any point on the circle `x^(2)+y^(2)=25` to the ellipse `(x^(2))/(16)+(y^(2))/(9)=1` are at right angle Statement-2: The locus of the point of intersection of perpendicular tangents to an ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` is its director circle
`x^(2)+y^(2)=a^(2)+b^(2)`.

A

Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1

B

Statement-1 is True, Statement-2 is True, Statement -2 is not a correct explanation for Statement-1

C

Statement-1 is True, Statement-2 is False.

D

Statement-1 is False, Statement-2 is True

Text Solution

Verified by Experts

The correct Answer is:
A
Statement-2 true (see Section 11 on page 25.16) Clearly. `x^(2)+y^(2)=25` is the director circle of the ellipse `(x^(2))/(16)+(y^(2))/(9)=1` So, tangents drawn from any point on `x^(2)+y^(2)=25` to the ellipse are at right angle. So, statement-1 is true. Also, statement-2 is correct explanation fro statement-1`.
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