Question

Find the equation of chord of contact of the point (3, 5) on the circle $x^2+y^2+12x+8y+7=0$.

• A. 9x - y - 5 = 0
• B. 9x + y + 5 = 0
• C. 13 x + 2y - 1 = 0
• D. 13x - 2y +1 =0

Answer 1

The correct option is B

9x + y + 5 = 0

For finding the chord of contact the easiest method is to make use of the expression $T_1$.

We have equation of chord of contact as $T_1$ = 0.

$T_1$ is obtained by replacing $x^2$ in the equation of circle by $x{x}_1,y^{2}byy{y}_1,xby\frac{x+x_1}{2},yby\frac{y+y_1}{2},,xybyx{y}_1+\frac{y{x}_1}{2}$, where $(x_1,y_1)$ is the external point.

Hence for a general circle $x^2+y^2+2gx+2fy+c=0$, the equation of chord of contact will be

$x{x}_1+y{y}_1+g(x+x_1)+f(y+y_1)+c=0$

Applying it here,

$(x_1,y_1)\equiv (3,5)$

Given circle: $x^2+y^2+12x-8y+7=0$

Required equation $\Rightarrow$

$T_1=0$

i.e., $3x+5y+6(x+3)-4(y+5)+7=0$

$9x+y+18-20+7=0$

$9x+y+5=0$