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Question:
Find the coordinates of the focus and the vertex, the equations of the directrix and the axis, and length of the latus rectum of the parabola :
$x^{2}=-8 y$
Solution:
Given equation : $x^{2}=-8 y$
Comparing given equation with parabola having equation,
$x^{2}=-4 a y$
$4 a=8$
$\cdot a=2$
Focus: $F(0,-a)=F(0,-2)$
Vertex : $A(0,0)=A(0,0)$
Equation of the directrix : $y-a=0$
- $y-2=0$
- $y=2$
Lenth of latusrectum : $4 a=8$
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