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 :
$x^{2}=10 y$
Solution:
Given equation : $x^{2}=10 y$
Comparing given equation with parabola having equation
$x^{2}=4 a y$
$4 a=10$
$\cdot a=2.5$
Focus : $F(0, a)=F(0,2.5)$
Vertex : $A(0,0)=A(0,0)$
Equation of the directrix : $y+a=0$
$-y+2.5=0$
$\cdot y=-2.5$
Lenth of latusrectum : 4a = 10
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