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The circle with equation x^2 +y^2 = 1 in...

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

A

`tan^(-1)((4)/(3))`

B

`tan^(-1)((3)/(4))`

C

`pi//4`

D

`tan^(-1)((3)/(2))`

Text Solution

Verified by Experts

The correct Answer is:
C

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)`
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