question_answer

The locus of the middle points of the focal chords of parabola, \[{{y}^{2}}=8x\]is another parabola whose length of latus rectum is

A) 1      

B)                                    2

C) 3            

D)                                    4

Correct Answer: D

Solution :

\[2h=a({{t}_{1}}^{2}+t_{2}^{2})\]                             ?(i) \[2k=2a({{t}_{1}}+{{t}_{2}})\]                     ?(ii) and \[{{t}_{1}}{{t}_{2}}=-1\] from (2) \[{{k}^{2}}={{a}^{2}}\left[ \frac{2h}{a}-2 \right]\] \[{{y}^{2}}=2a(x-2a)\] Put \[16x-12y+12=0\] Hence, \[{{y}^{2}}=4(x-4)\]