If a chord , which is not a tangent of the parabola `y^2=16x` has the equation 2x+y=p, and mid-point (h,k), then which of the following is (are) possible values (s) of p,h and k?

Options

A. `p=5, h=4, k=-3`
B. `p=-1, h=1, k=-3`
C. `p=-2, h=2, k=-4`
D. `p=2, h=3, k=-4`

Answer

D

Explanation

The chord 2x+y=p has (h, k) as its mid-point. So, its equation is
`k^(2)-16h=ky-8(x+h)" "["Using S'=T"]`
or, `ky-8x=k^(2)-8h" …(i)"`
It is given that 2x+y=p and (i) represent the same line.
`:." "2/(-8)=1/k=p/(k^(2)-8k)`
`rArr" "k=-4" and "k^(2)-8h=-4p`
`rArr" "k=-4" and "2h-p=4`
Clearly, values in option (d) satisfy these equations.