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Question

Find the equation of chord of parabola
y2 = 4x whose midpoint is (4, 2)


A

xy+2=0

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B

x+y+2=0

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C

2x+y4=0

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D

xy2=0

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Solution

The correct option is D

xy2=0


Equation of the chord of the parabola y2 = 4ax whose middle point is (x1 , y1) is

T = S1

yy1 2a(x+x1) = y21 4ax1

yy1 y21 = 2ax + 2ax1 4ax1

y1(y y1) = 2a(x x1)

y y1 = 2ay1(x x1)

substituting ,x1 = 4,y1 = 2 and a = 1

y 2 = 22(x 4)

y 2 = x 4

x y 2 = 0


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