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Q.

A tangent to the parabola y2=4ax meets the x-axis in T and the tangent at the vertex A in P. If TAPQ is a rectangle, then the locus of Q is

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a

y2+ax=0

b

y2-2ax=0

c

2y2-ax=0

d

x2+ay=0

answer is B.

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Detailed Solution

Given parabola y2=4ax Let Q be (h,k),T(-h,0)  and  P(0,k)   Let the tangent be, y=mx+am   am=hm m2=ah...(1)   am=km=ak...(2)   From (1)  and (2)   a2k2=ah   ah=-k2 locus of Q(h,k) is   ax=y2 y2+ax=0  Question Image

 

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A tangent to the parabola y2=4ax meets the x-axis in T and the tangent at the vertex A in P. If TAPQ is a rectangle, then the locus of Q is