Question

The ends of latus rectum of parabola $x^2+8y=0$

• A. (-4, -2) and (4, 2)
• B. (-4, -2) and (-4, 2)
• C. (-4, -2) and (4, -2)
• D. (4, -2) and (-4, 2)

Answer 1

The correct option is C (-4, -2) and (4, -2)

$x^2=-8y\Rightarrow a=-2.So,focus=(0,2)$
Latus rectum is the chord which passes through the focus and is perpendicular to the axis. Given parabola is of the form $x^2=4ay$. Focus of the this parabola is (0,a) and the axis is y-axis or the line x=0. The points where this line intersects the parabola is the end points of parabola.
=> (2a, a) and (-2a,a) are the end points.
$x^2=-8y\Rightarrow a=-2.$
Ends of latus rectum = (4, -2), (-4, -2)