question_answer

The locus of the foot of the perpendiculars drawn from the vertex on a variable tangent to the parabola \[{{y}^{2}}=4ax\] is

A)  \[x({{x}^{2}}+{{y}^{2}})=a{{y}^{2}}=0\]           

B)  \[y({{x}^{2}}+{{y}^{2}})=a{{x}^{2}}=0\]

C)  \[x({{x}^{2}}-{{y}^{2}})+a{{y}^{2}}=0\]

D)  \[{{x}^{2}}+{{y}^{2}}+a{{y}^{2}}=0\]