Question

If the parabola y² = 4ax passes through the point (3, 2), then find the length of its latus rectum.

Answer 1

We have y² = 4ax
Since, the parabola is passing through the point (3, 2)
Hence, it will satisfy the equation of the parabola.
∴ 2² = 4(a)(3)
$\Rightarrow a=\frac{1}{3}$
Lenth of the latus ractum is given by
$$\begin{gathered} 4a \\ =4\times \frac{1}{3} \\ =\frac{4}{3} \end{gathered}$$