question_answer

Length of the normal chord of the parabola, \[{{y}^{2}}=4x\], which makes an angle of \[\frac{\pi }{4}\] with the axis of \[x\] is

A)  8                                

B)  \[8\sqrt{2}\]

C)  4                                

D)  \[4\sqrt{2}\]

Correct Answer: B

Solution :

\[N:y+tx=2t+{{t}^{3}};\] slope of the normal is - t Hence \[-t=1\Rightarrow \,t=-1\] \[\Rightarrow \] coordinates of P are (1, -2) Hence parameter at Q, \[{{t}_{2}}=-{{t}_{1}}-2/{{t}_{1}}=1+2=3\] \[\therefore \] coordinates at Q are (9, 6) \[\therefore \] \[l(PQ)\,=\sqrt{64+64}\,=8\sqrt{2}\]