Q.

If the normal at one end of the latus rectum of the parabola y2=16x meets the X-aixs at the point P, then the length of the chord passing through P and perpendicular to the normal is

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a

482 

b

202

c

242

d

322 

answer is B.

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Detailed Solution

y2=16x one end of latusrectum  L=(a,2a)=(4, 8) Normal at (4, 8)  is  y-y1=-y12a(x-x1)         y-8=-88(x-4) x+y-12=0 It meets x-axis at P=(12, 0)

Equation of the chord passing through P(12, 0) tr to normal is y=1(x-12)

Length of chord =x1-x21+m2

(x-12)2=16x x2-40x+144=0 x1-x2=1a=1600-576=32 Length of chord = 322

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