• # question_answer Statement 1: The circles ${{x}^{2}}+{{y}^{2}}=9$ and $(2x-3)(x-1)+2y(y-\sqrt{6})=0$ touches each other internally.  Statement 2: Circle described on the focal distance as diameter of the ellipse $8{{x}^{2}}+9{{y}^{2}}=72$ touches the auxiliary circle ${{x}^{2}}+{{y}^{2}}=9$ internally. A)  Statement-1 is true, Statement-2 is true and Statement-2 is correct explanation for Statement-1. B)  Statement-1 is true, Statement-2 is true and Statement-2 is NOT the correct explanation for Statement-1. C)  Statement-1 is true, Statement-2 is false D)  Statement-1 is false, Statement-2 is true

Equation of ellipse in $\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{8}=1$ Focus $\equiv (1,\,0),\,e=\frac{1}{3}$ Also, a point on given ellipse is $\left( 3\cos \theta ,\,\,2\sqrt{2}\,\sin \theta \right)$ Put $\theta =\frac{\pi }{3}$, we get a point on given ellipse as $\left( \frac{3}{2},\,\sqrt{6} \right)$. Now, circle described on the focal distance as diameter of the ellipse is $(2x-3)\,(x-1)\,+2y\left( y-\sqrt{6} \right)=0$ Which is true. (Using property of ellipse.)