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Question

The normal at P(2,4) to y2=8x meets the parabola at Q. Then the equation of the circle having normal chord PQ as diameter is

A
x2+y220x+8y12=0
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B
x2+y210x+4y8=0
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C
x2+y212x+6y15=0
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D
x2+y210x+8y12=0
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Solution

The correct option is A x2+y220x+8y12=0
Normal at (at21,2at1) meets the parabola again at (at22,2at2)
Then, t2=t12t1
Given parabola is y2=8x
a=2
We are given P=(2,4)
2at1=4
t1=1
t2=t12t1
t2=3
Then, P=(2,4) and Q=(18,12)
Then, equation of circle is given by (x2)(x18)+(y4)(y+12)=0
x2+y220x+8y12=0

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