Q. The equation of pair of lines joining origin to the points of intersection of $x^{2} + y^{2} = 9$ and $x + y = 3$ is
A) $x^{2} + {(3 - x)}^{2} = 9$
B) $xy = 0$
C) ${(3 + y)}^{2} + y^{2} = 9$
D) ${(x - y)}^{2} = 9$
Explanation
(b)
Given, $x^{2} + y^{2} = 9$ …(i)
and $x + y = 3$ …(ii)
From Eqs. (i) and (ii), we make a homogeneous equation.
$\Rightarrow \ x^{2} + y^{2} = (x + y)^{2}$
$\Rightarrow \ x^{2} + y^{2} = x^{2} + y^{2} + 2xy$
$\Rightarrow \ xy = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.