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 :

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 = 10y

Philoid · Accepted Answer

Given equation : x² = 10y

Comparing given equation with parabola having equation,

x² = 4ay

4a = 10

• 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

• y = -2.5

Lenth of latusrectum : 4a = 10

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 :x2 = 10y

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 :
x² = 10y