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???

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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(-2,0)

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