question_answer

If the angle between the normal to the parabola \[{{x}^{2}}=4ay\] at point P and the focal chord passing through P is \[\frac{\pi }{3},\] then the slope of the tangent at point P is

A) \[1/\sqrt{3}\]        

B)                    \[\sqrt{3}\]                  

C) \[\sqrt{2}\]                   

D)        \[1/\sqrt{2}\]

Correct Answer: B

Solution :

[b] By property, tangent PT bisects the angle \[\angle SPM.\] Given that \[\angle SPM=60{}^\circ \] \[\therefore \,\,\,\,\,\angle SPT=\angle TPM=30{}^\circ \] So, tangent makes an angle \[60{}^\circ \] with x-axis. \[\therefore \] Slope of tangent \[=\sqrt{3}\]