question_answer

    AB is a chord of the parabola\[{{y}^{2}}=4ax\]with vertex at A. BC is drawn perpendicular to AB meeting the axis at C. The projection of BC on the axis of the parabola is

A)  2                                            

B)  \[2a\]

C)  \[4a\]                                  

D)  \[8a\]

Correct Answer: C

Solution :

                In\[\Delta ABC,\]we have \[\tan \theta -\frac{y}{x}\]               ...(i) In\[\Delta BCD,\]we have                 \[\tan (90{}^\circ -\theta )=\frac{y}{CD}\] \[\Rightarrow \] \[CD=y\,\tan \theta =\frac{{{y}^{2}}}{x}\]           [using Eq. (i)] \[\Rightarrow \]               \[CD=\frac{4ax}{x}=4a\]