Question

find the locus of Mid-point of normal chord to the parabola y2=4ax

Answer 1

Step-by-step explanation:

Let AB be a normal chord where A≡(at12,2at1) and B≡(at22,2at2).

Let the midpoint of AB is P(h,k), then

2h=a(t12+t22)

    =a[(t1+t2)2−2t1t2]

and   2k=2a(t1+t2)

We also have,

t2=−t1−t12

⇒t1+t2=t1−2 and t1t2=−t12−2

⇒ak=t1−2

Answer 2

Answer:

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