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Q.

If chord, which is not a tangent, of the parabola y2=16x has the equation, 2x+y=p and midpoint,h,k the which of the following is (are) possible values (S) of p,h,k

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a

p=2, h=3, k=−4

b

p=5, h=4, k=−3

c

p=−1, h=1, k=−3

d

p=−2, h=2, k=−4

answer is A.

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Detailed Solution

S1=S11ky−8x+h=k2−16hky−8x+8h−k2=0−ky+8x+k2−8h=0Comparing the given equation y+2x−p=0−k1=4=k2−8h−p−k1=4=k2−8h−p−4p=k2−8h and 8h−4p=162h−p=4Verify the options

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If chord, which is not a tangent, of the parabola y2=16x has the equation, 2x+y=p and midpoint,h,k the which of the following is (are) possible values (S) of p,h,k