if tangent at point p(2,4)to parabnola ysq.=8x meet ysq=8x+5 at q r is the midpoint of pq them find r?

Hi Akhilesh,

The Eqn of Tangent is T=0

ie 4y = 4(x+2), which meets the parabola y²=8x+5.

Solve the line Eqn with the 2nd Parabola, y²=8y-11

y²-8y+11=0

y = {8 (+/-) √20}/2

Correspondingly you'll get two values of x = y-2.

So there are two points where the line would meet the Parabola at "Q1" and "Q2".

Find the corresponding two midpoints.(Please do the Calculation on your own).

Else if your question was to the find the midpoint of the points where the Tangent meets the parabola, then y1+y2=8

And x1+x2=y1+y2-4 = 4

So midpoint would be (2,4)-------- of the two points, where the Tangent meets the second parabola.

Hope that helps.

Best Regards,

Ashwin (IIT Madras).