The line `y = mx` intersects the circle `x^(2)+y^(2) -2x - 2y = 0` and `x^(2)+y^(2) +6x - 8y =0` at point A and B (points being other than origin). The range of m such that origin divides AB internally is

Options

A. `-1 lt m lt (3)/(4)`
B. `m gt (4)/(3)` or `m lt -2`
C. `-2 lt m lt (4)/(3)`
D. `m gt -1`

Answer

A

Explanation

The tangents at the origin to `C_(1)` and `C_(2)` are `x +y =0, 3x -4y =0`, respectively.
Slope of the tangents are `-1` and `(3)/(4)`, respectively.
Then if `-1 lt m lt (3)/(4)`, then origin divides AB internally.