Question

If the tangents are drawn from any point on the line $x+y=3$ to the circle $x^2+y^2=9$, then the chord of contact passes through the point

• A. $(3,5)$
• B. $(3,3)$
• C. $(5,3)$
• D. None of these

Answer 1

The correct option is B $(3,3)$

Let $(\alpha ,3-\alpha )$ be any point on $x+y=3$.
$\therefore$ Equation of chord of contact is $\alpha x+(3-\alpha )y=9$
i.e., $\alpha (x-y)+3y-9=0$
$\therefore$ The chord passes through the point $(3,3)$ for all values of $\alpha$.