question_answer

The normal at the point \[(bt_{1}^{2},b{{t}_{1}})\] on a parabola meets the parabola again in the point\[(bt_{2}^{2},2b{{t}_{2}})\], then     AIEEE  Solved  Paper-2003

A) \[{{t}_{2}}=-{{t}_{1}}-\frac{2}{{{t}_{1}}}\]     

B)       \[{{t}_{2}}=-{{t}_{1}}+\frac{2}{{{t}_{1}}}\]                            

C) \[{{t}_{2}}={{t}_{1}}-\frac{2}{{{t}_{1}}}\]      

D)       \[{{t}_{2}}={{t}_{1}}+\frac{2}{{{t}_{1}}}\]

Correct Answer: A

Solution :

Equation of normal at a point () on a parabola  is . Equation of the normal at point  on parabola is  It also passes through , then                                                                                                   NOTE If a normal drawn at a point \[{{t}_{1}}\] on the parabola meets the parabola again at a point \[{{t}_{2}}\], then