A chord of a parabolaIf 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 values of p,h and k?A):p=−2,h=2,k=−4B):p=−1,h=1,k=−3C):p=2,h=3,k=−4D):p=5,h=4,k=−3If I do it by mid point of chord formula i.e. S1=T then I get C) as answer, which is actually correct.If I use the intersecting line concept i.e. c&lt;am then I don't get any answer. Why?

Question

A chord of a parabolaIf 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 values of p,h and k?A):p=−2,h=2,k=−4B):p=−1,h=1,k=−3C):p=2,h=3,k=−4D):p=5,h=4,k=−3If I do it by mid point of chord formula i.e. S1=T then I get C) as answer, which is actually correct.If I use the intersecting line concept i.e. c&amp;lt;am then I don&#039;t get any answer. Why?

Tommie Bryan · Accepted Answer

Since 2x=p−y, we obtain:y2=8(p−y)or y2+8y−8p=0,which gives y1+y2=−8and k=y1+y22=−4.If p=−2 we obtain:y2+8y+16=0or (y+4)2=0,which gives that 2x+y=p is a tangent to the parabola, which is impossible.

A chord of a parabola If a chord, which is not a tangent, of the parabola y^2=16x has the

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