If the angle of intersection of the circle `x^2+y^2+x+y=0` and `x^2+y^2+x-y=0` is `theta` , then the equation of the line passing through (1, 2) and making an angle `theta` with the y-axis is `x=1` (b) `y=2` `x+y=3` (d) `x-y=3`

Options

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

Answer

2

Explanation

Let A and B be the centers and `r_(1)` and `r_(2)` be the radii of the two circles. Then ,
`A-=(-(1)/(2),-(1)/(2)),B-=(-(1)/(2),(1)/(2)),`
`r_(1)=(1)/(sqrt(2)),r_(2)=(1)/(sqrt(2))`
`cos theta =(r_(1)^(2)+r_(2)^(2)-AB^(2))/(2r_(1)r_(2))`
`=((1)/(2)+(1)/(2)-1)/(2xx(1)/(sqrt(2))xx(1)/(sqrt(2)))=0`
or `theat =(pi)/(2)`
Therefore, the required line is parallel to the x-axis and since it passes through (1,2), its equation will be y`=2`