Let A and B be two distinct points on the parabola `y^2=4x`. If the axis of the parabola touches a circle of radius r having AB as its diameter, then find the slope of the line joining A and B .

Options

A. `+-1/r`
B. `+-2/r`
C. `+-3/r`
D. `+-1/2r`

Answer

B

Explanation

Let `A(t_(1)^(2), 2t_(1))" and "B(t_(2)^(2), 2t_(2))` be two point on `y^(2)=4x`. The coordinates of the cetre of the circle are `((t_(1)^(2)+t_(2)^(2))/2,t_(1)+t_(2))`
Since the circle with diameter AB touches the axis of the parabola and is of radius r.
`:. "t_(1)+t_(2)=+r`
`:." Slope of AB"2/(t_(2)+t_(1))=+-2/r`