If the lines joining the origin to the points of intersection of the line `y=mx+2` and the curve `x^(2)+y^(2)=1` are at right-angles, then

Options

A. `m^2=1`
B. `m^2=3`
C. `m^2=7`
D. `2m^2=1`

Answer

C

Explanation

The joint equation of lines joining the origin and the point of intersection of the line `y=mx+2`andthe curve `x^2+y^2=1` is
`x^2+y^2=((y-mx)/(2))^2rArr 4(x^2+y^2)=(y-mx)^2`
`rArr x^2(4-m^2)+2mxy+3y^2=0`
The lines given by the above equation are at right angles.
`therefore 4-m^2+3=0rArr m^2=7" "[because "condition for right angle" ,a+b=0]`