question_answer

The length of a focal chord of the parabola \[{{y}^{2}}=4ax\]at a distance b from the vertex is c, then

A)   \[2{{a}^{2}}=bc\]           

B)     \[{{a}^{3}}={{b}^{2}}c\]

C)  \[ac={{b}^{2}}\]           

D)     \[{{b}^{2}}c=4{{a}^{3}}\]

Correct Answer: D

Solution :

                        Given \[l(PQ)=c\]             \[\cos ec\theta \,=\frac{a}{b}\]             Now \[c=4a\,\cos e{{c}^{2}}\theta \]             \[c=4a.\,\,\frac{{{a}^{2}}}{{{b}^{2}}};\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,4{{a}^{3}}\,={{b}^{2}}c\]