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Question

If one end of focal chord PQ of the parabola y2=8x is at P(12,2), then the equation of tangent to it at Q is

A
x+2y+8=0
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B
2xy24=0
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C
x2y+8=0
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D
2x+y24=0
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Solution

The correct option is C x2y+8=0
PQ is the focal chord of the parabola y2=8x
P(t1)=(2t21,4t1), Q(t2)=(2t22,4t2)
t1t2=1

(12,2)=(2t21,4t1)t1=12t2=2

So, Q=(8,8)
The equation of the tangent at Q is
T=08y=4(x+8)x2y+8=0

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