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

(p-6x)²=16x ⇒p²-8px+4x²=16x ⇒4x²+x(-8p-16)+p²=0 ⇒x₁+x₂=4p+16/4=p+4 ∴h=x₁+x₂/2=p+4/2
y₁+y₂/2=p-6x₁+p-6x₂/2=p-(x₁+x₂) ∴k=p-(p+4)=-4
So, we have to check between options C and D.
Option C: p=6,h=2 ⇒x₁+x₂=2h=4 ⇒k=p-(x₁+x₂)=6-4=2≠-8
Hence, option C is not correct.
Option D: p=2,h=3 ⇒x₁+x₂=2h=6 ⇒k=p-(x₁+x₂)=2-6=-4≠-8
Hence, option D is not correct. Let's re-examine the solution for k.
The midpoint of the chord is (h,k) and the equation of the chord is 2x+y=p. Substituting the midpoint, we get 2h+k=p. Then k=p-2h.
Option A: p=5, h=4, k=-7. Then k = 5 - 2(4) = -3 ≠ -7. Incorrect.
Option B: p=6, h=2, k=-8. Then k = 6 - 2(2) = 2 ≠ -8. Incorrect.
Option C: p=2, h=3, k=-8. Then k = 2 - 2(3) = -4 ≠ -8. Incorrect.
Option D: p=5, h=1, k=-7. Then k = 5 - 2(1) = 3 ≠ -7. Incorrect.
Let's reconsider the derivation of the midpoint. The equation of the chord is y = p - 2x. Substitute into y² = 16x to get (p-2x)² = 16x.
4x² - 4px + p² = 16x
4x² - (4p+16)x + p² = 0
The sum of the roots is x₁ + x₂ = (4p+16)/4 = p+4.
The midpoint's x coordinate is h = (x₁+x₂)/2 = (p+4)/2.
The midpoint's y coordinate is k = (y₁+y₂)/2 = (p-2x₁+p-2x₂)/2 = p - (x₁+x₂)= p - (p+4) = -4.
Therefore, k = -4 for all options. None of the given options are correct.