Question

The latus rectum of the focus of the parabola $y^2 = 5x + 4y + 1$ is

Answer 1

5

Answer 2

The given equation of the parabola is $y^2 = 5x + 4y + 1$. Rearranging and completing the square for the $y$ terms: $y^2 - 4y = 5x + 1$ $(y^2 - 4y + 4) - 4 = 5x + 1$ $(y-2)^2 = 5x + 5$ $(y-2)^2 = 5(x+1)$

This is in the standard form $(y-k)^2 = 4a(x-h)$, where $4a = 5$. The length of the latus rectum is $|4a|$. Therefore, the length of the latus rectum is $|5| = 5$.