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Question

Find the locus of the middle points of all chords of the parabola y2=4ax which are drawn through the vertex.

A
2y2=ax
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B
y2=2ax
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C
y2=4ax
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D
y2=ax
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Solution

The correct option is A y2=2ax
Vertex is V(0,0) and any point on the parabola is P(at2,2at)
Now mid point of chord VP is R(at22,at)
Let locus of R is (x,y)
x=at22,y=at
Elimination t we get required locus y2=2ax

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