Question

The point (2, 3) is a limiting point of a coaxial system of circles of which $x^2+y^2=9$ is a member. The co-ordinates of the other limiting point is given by

• A. $(\frac{18}{13},\frac{27}{13})$
• B. $(\frac{9}{13},\frac{6}{13})$
• C. $(\frac{18}{13},-\frac{27}{13})$
• D. $(-\frac{18}{13},-\frac{9}{13})$

Answer 1

The correct option is A

$(\frac{18}{13},\frac{27}{13})$

$(x-2{)}^2+(y-3{)}^2=0$

or $(x^2+y^2-9)-4x-6y+22=0$

or $(x^2+y^2-9)-\lambda (2x+3y-11)=0$ represents the family of co-axial circles.

C = $(\lambda ,\frac{3\lambda }{2})$, $r=\sqrt{{\lambda }^2+\frac{9{\lambda }^2}{4}-11\lambda +9}$