Question

The area of the triangle formed by the polar of $(1,2)$ with respect to the circle $2x^2+2y^2$ -3x $=0$ and the coordinate axes is

• A. $\frac{3}{16}$ sq. units
• B. $\frac{9}{16}$ sq.units
• C. $\frac{3}{8}$ sq. units
• D. $\frac{9}{112}$ sq.units

Answer 1

Answer: (B)

$\frac{9}{16}$ sq.units

Polar of (1,2) with respect to circle $2x^2+2y^2-3x=0$ is
equation of chord of contact from (1,2) to circle $2x^2+2y^2-3x=0$
then, $2x{x}_1+2y{y}_1-\frac{3}{2}(x+x_1)=0$ is equation of chord
$\therefore$ of chord of contact to $2(x^2+y^2)-3x=0fromp(x_1,y_1)$
$\therefore 2x+2y\times 2-\frac{3}{2}(x+1)=0$
$4x+8y-3x-3=0$
$x+y-3=0$
then, area of triengle formed by $x+8y=3$ with
co ordinate ones $=\frac{1}{2}\times \frac{3}{8}\times 3$
$=\frac{9}{2\times 8}$
$=\frac{9}{16}$ sq units