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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???
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)
what is the answer ?In want to deal this q with u.
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