Question

If the angle of intersection of the circles $x^2+y^2+x+y=0$ and $x^2+y^2+x-y=0$ is $\theta$, then equation of the line passing through $(1,2)$ and making an angle $\theta$ with the y-axis is

• A. $x=1$
• B. $y=2$
• C. $x+y=3$
• D. $x-y=3$

Answer 1

Answer: (A)

$x=1$

Let $S_1:x^2+y^2+x+y=0$ and $S_2:x^2+y^2+x-y=0$
Intersection points of the circle are $(0,0),(-1,0)$
Now slope of tangents at $(0,0)$ to $S_1$ is $m_1=-1$ and slope of tangent to $S_2$ at the same point is $m_2=1$
Clearly, $m_1{m}_2=-1\Rightarrow \theta ={90}^0$
Hence required equation of line passes through $(1,2)$ and making angle ${90}^0$ with $y-$ axis is given by, $x=1$