Question

The common chord of $x^2+y^2-4x-4y=0$ and $x^2+y^2=16$ subtends at the origin an angle equal to

• A. $\frac{\pi }{6}$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{3}$
• D. $\frac{\pi }{2}$

Answer 1

Answer: (D)

$\frac{\pi }{2}$

Let $S_1:x^2+y^2-4x-4y=0$

and $S_2:x^2+y^2-16=0$

$\therefore$ Equation of common chord is

$S_1-S_2=0\Rightarrow -4x-4y+16=0\therefore x+y=4$

which is a line equally inclined to the axes.

$\therefore$ Angle subtends by common chord at origin is $\frac{\pi }{2}$