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 = -8y

Philoid · Accepted Answer

Given equation : x² = - 8y

Comparing given equation with parabola having equation,

x² = - 4ay

4a = 8

• 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 : 4a = 8

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 = -8y

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 = -8y