Q. A circle of radius , drawn on a chord of the parabola as diameter, touches the axis of the parabola. Then, the slope of the chord is

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Solution:

Given, equation of parabola is
...(i)

Let be the coordinate of mid-point of chord.
Then, equation of chord is
...(ii)
If line (ii) passes through the point and on parabola Eq. (i), then
...(iii)
having slope
...(iv)
Since, is the mid-point of . Therefore,


Hence, slope of chord is
[using Eq. (iv)]