Question

Let the particle starts from the point $(2,0)$ and moves $\frac{\pi }{2}$ units, on circle $C_2$ in the counter-clockwise direction, then moves on the circle $C_3$ along the tangential path, let this straight line(tangential path traced by particle) intersect the circle $C_3$ at the points $A$ and $B$ and tangents drawn at $A$ and $B$ intersect at

• A. $(\frac{9}{2\sqrt{2}},\frac{9}{2\sqrt{2}})$
• B. $(9\sqrt{2},9\sqrt{2})$
• C. $(9,9)$
• D. $(\sqrt{2},\sqrt{2})$

Answer 1

The correct option is A $(\frac{9}{2\sqrt{2}},\frac{9}{2\sqrt{2}})$

Co-ordinates of $C$ are
$(2\cos \frac{\pi }{4},2\sin \frac{\pi }{4})$ [ $\because$ Using parametric value]
$=(\sqrt{2},\sqrt{2})$
$\therefore$ Equation of tangent AR is $x+y=x\sqrt{2}$
$\therefore$ The intersect the circle $x^2+y^2=9$ at $A$ and $B$.
$P\equiv (\frac{9}{2\sqrt{2}},\frac{9}{2\sqrt{2}})$