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# if the tangent at the point P(2,4) to the parabola y2=8x meets the parabola y2=8x+5 at Q and R then the mid-point of QR is???

## 3 Answers

10 years ago

equation of tangent to parabola is

yy1 = 8(x+x1)/2

(x1,y1) = (2,4)

4y = 4(x+2)

y = x + 2       ....................1

this line intersects y2 = 8x + 5 at two points , let these points be P,Q then

P = (x1,y1) &  Q = (x2,y2)

y = x+2

y2 = 8x + 5

from these two equations we get

x2 - 4x - 1 = 0                 &                      y2 - 8y - 11 = 0

x1+x2 = 4                                               y1+y2 = 8

midpoint of Q,R will be [(x1+x2)/2 , (y1+y2)/2] = (2,4)

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