Question

# In the parabola y2=4 ax, the length of the chord passing through the vertex and inclined to the axis at π4 is

A

42a

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B

22a

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C

2a

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D

none of these

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Solution

## The correct option is A 4√2a Let OP be the chord. Let the coordinates of P be (x1,y1) From the figure, we have: OP2=x21+y21 ...(1) And,tanπ4=y1x1 ⇒ x1=y1 ...(2) Also,(x1,y1) lies on the parabola. ∴ y21=4ax1 ...(3) Using (2) and (3) : x21=4ax1⇒x1=4a ...(4) ∴ From (4),(1) and (2),we have: OP2=(4a)2+(4a)2=32a2 ⇒ OP=4√2a Therefore,the length of the chord is 4√2a units.

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