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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)=225` to the ellipse `(x^(2))/(144)+(y^(2))/(81)=1` are at a right angle.
Statement -2 : Equation of the auxiliary circle of the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1 " is " x^(2)+y^(2)=a^(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:
B
As `x ^(2)+y^(2)=225` is the director circle of the ellipse `(x^(2))/(144)+(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 (see section 6 on page 25. 8). But, it is not an explanation for statement-1.
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