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 the slope of the line joining `A and B` can be (A) `- 1/r` (B) `1/r` (C) `2/r` (D) `- 2/r`

Options

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

Answer

C, D

Explanation

3,4

We have points `A(t_(1)^(2),2t_(1))andB(t_(2)^(2),2t_(2))` on the parabola `y^(2)=4x`.
For circle on AB as diameter center is `C((t_(1)^(2)+t_(2)^(2))/(2),(t_(1)+t_(2)))`.
Since circle is touching the x-axis, we have `r=|t_(1)+t_(2)|`
Also slope of AB, m `=(2t_(1)-2t_(2))/(t_(1)^(2)-t_(2)^(2))=(2)/(t_(1)+t_(2))=pm(2)/(r)`