Question

If the `y=mx+1,` of the circle `x^2+y^2=1` subtends an angle of measure `45^@` of the major segment of the circle then value of `m` is -
A. 2
B. `-2`
C. `-1`
D. none of these

Answer 1

Correct Answer - 3
The given circle is `x^(2)+y^(2)=1`. Center, `C-=(0,0)` radius `=1`, and chord is `y=mx+1`.
`cos 45^(@)=(CP)/(CR)`

Perpendicular distance from `(0,0)` to the chord `y=mx+1`
`CP=(1)/(sqrt(m^(2)+1))`
or `cos 45^(@)=(1//sqrt(m^(2)+1))/(1)`
or `(1)/(sqrt(2))=(1)/(sqrt(m^(2)+1))`
or `m^(2)+1=2`
or `m= +-1`