Question

A chord of contact of a point P(k, 2k) is drawn with respect to the circle $x^2+y^2+2x+2y-9=0$. What is the value of 'k' if the chord passes through the origin?

• A. -1
• B.
• C. 3
• D. -5

Answer 1

The correct option is C

3

Lets draw the circle, point and the chord of contact first.

The equation of chord of contact can be found by $T_1=0$ where $T_1$ is an expression that you get when you replace

• $x^{2}byx{x}_1$
• $y^{2}byy{y}_1$
• $xby\frac{x+x_1}{2}$
• $yby\frac{y+y_1}{2}$
• $xyby\frac{x{y}_1+y{x}_1}{2}$ in a second degree polynomial

i.e., k.x+2k.y+(x+k)+(y+2k)-9=0

since this chord pass through origin we can give the value (0,0) to (x,y). Then the equation becomes.

0+0+(0+k)+(0+2k)-9=0

3k=9

$\therefore$k=3