Statement I : Circles $x^{2} + y^{2} = 9$ and $(x - \sqrt{5}) (\sqrt{2} x - 3) + y (\sqrt{2} y - 2) = 0$ touch each other internally.
Statement II : The circle described on the focal distance as diameter of the ellipse
$4 x^{2} + 9 y^{2} = 36$ touches the auxiliary circle $x^{2} + y^{2} = 9$ internally.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

Both statement I and II are true but statement II is the correct explanation of statement 1.

Both statement I and II are true but statement II is not the correct explanation of statement 1.

Statement I is true and statement II is false.

Statement I is false sand statement II is true.

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Statement II is true as it is one of the properties of ellipse.
Ellipse is $\frac{x^{2}}{9} + \frac{y^{2}}{4} = 1$
Focus $\equiv (\sqrt{5}, 0), e = \sqrt{5} / 3$
One of the points on the ellipse is $(3 / \sqrt{2}, 2 / \sqrt{2})$ .
The equation of the circle as the diameter joining the points $(3 / \sqrt{2}, 2 / \sqrt{2})$ and focus $(\sqrt{5}, 0)$ is