Question

IF tangents are drawn from any point on the lline x + y =3 to the circle $X^2+y^2=9$ then the chord of contract passes through the point

• A. (1,1)
• B. (2,2)
• C. (3,3)
• D. (4,4)

Answer 1

The correct option is C (3,3)

Given line $x+y=3$

circle $x^2+y^2=9$

Let assume (h, k) on line $x+y=3$

It satisfies equation $h+k=3$ ……..$\left(1\right)$ as it is on line

Lets draw tangents from (h, k( to circle $x^2+y^2=9$

Chord of contact will be $hx+ky=9$ ………..$\left(2\right)$

From $\left(1\right)$ & $\left(2\right)$

$h+k=3$ $hx+ky=9$

$\frac{h}{3}+\frac{k}{3}=1$ $\frac{hx}{9}+\frac{ky}{9}=1$

Comparing both

$\frac{x}{9}=\frac{1}{3}$ $\frac{y}{9}=\frac{1}{3}$

$x=3$ $y=3$

$\therefore$ The chord of contact always passes through point $(3,3)$.