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Q.

Let the tangent drawn to the parabola y2=24x at the point (α,β) is perpendicular to the line 2x+2y=5. Then the normal to the hyperbola x2α2y2β2=1 at the point (α+4,β+4) does not pass through the point :

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a

(30,8)

b

(20,12)

c

(15,13)

d

(25,10)

answer is D.

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Detailed Solution

Slope of the tangent to y2=24x at α,β=1 β2=24α,  Equation of tangent yβ=12x+α, Slope=12β=1 α=6,β=12(α+4,β+4)=(10,16) Normal at (10,16) to x236y2144=1 is36x10+144y16=36+144 2x+5y=100

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