question_answer

The equation of the latusrectum of the conic\[{{y}^{2}}=\frac{5}{2}x\]is

A)  \[8x-5=0\]

B)                         \[8x+5=0\]

C)  \[5x+8=0\]        

D)         \[x-5=0\]

E)  \[x-8=0\]

Correct Answer: A

Solution :

Given equation of conic, \[{{y}^{2}}=\frac{5x}{2}\] the length of focal\[\Rightarrow \]\[\frac{5}{8}\]                              \[\left( \because 4a=\frac{5}{2} \right)\] \[\Rightarrow \]               \[x=\frac{5}{8}\] So, equation of latusrectum is, \[8x-5=0\]