question_answer

The distance of two points P and Q on the parabola \[{{y}^{2}}=4ax\]from the focus S are 3 and 12. Then the distance of the point of intersection of the tangents at P and Q from the focus S is

A)  8                                            

B)  6

C)  9                                            

D)  12

Correct Answer: B

Solution :

 if \[P(a{{t}_{1}}^{2},2a{{t}_{1}})\]and \[Q(a{{t}_{2}}^{2},2a{{t}_{2}}),\]and \[T(a{{t}_{1}}{{t}_{2}},a({{t}_{1}}+{{t}_{2}}))\] \[\therefore \]  \[S{{T}^{2}}=SP.SQ=3\times 12=36\] \[\therefore \]  \[ST=6\]