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Question

# If a tangent to the parabola y2=4ax meets the x-axis at T and the tangent at the vertex A, at P. Let the rectangle TAPQ be completed. Then the locus of the point Q is

A

a circle

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B

a straight line

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C

a parabola

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D

an ellipse

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Solution

## The correct option is C a parabola The tangent at any point B(at2,2at) to the parabola is ty=x+at2 .......(1) Since tangent at the vertex A is the y-axis, T and P are (−at2,0) and (0,at) respectively. Clearly A is (0, 0) If Q be(h, k), then h =AT =−at2 and k= AP = at Eliminating t, we get k2+ah=0 Hence the locus of Q is y2+ax=0, which is parabola.

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