Question

The parabola $y^2=4ax$ passes through the point $(2,-6)$, then the length of its latus rectum is

• A. $9$
• B. $16$
• C. $18$
• D. $\frac{9}{2}$

Answer 1

The correct option is C $18$

in this equation of parabola is $y^2=4ax$ and the point is $(2,-6)$

substitute $x=2,y=-6$ in the equation of parabola

then we get,

$y^2=4ax$

$\Rightarrow 4a=\frac{y^2}{x}$

$\Rightarrow 4a=\frac{36}{2}$

$\Rightarrow 4a=18$

hence the length of its latus rectum is $18$.