The circle with equation `x^2 +y^2 = 1` intersects the line `y= 7x+5` at two distinct points A and B. Let C be the point at which the positive x-axis intersects the circle. The angle ACB is

Options

A. `tan^(-1)((4)/(3))`
B. `tan^(-1)((3)/(4))`
C. `pi//4`
D. `tan^(-1)((3)/(2))`

Answer

C

Explanation

Solving `y = 7x +5` and the circle `x^(2)+y^(2) =1`, we get
`A (-(3)/(5),(4)/(5))` and `B(-(4)/(5),-(3)/(5))`
`m_(OA) = -(4)/(3)` and `m_(OB) =(3)/(4)`
Hence, `/_AOD = 90^(@) rArr /_ACB = (pi)/(4)`