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 : y 2 = -8x

Philoid · Accepted Answer

Given equation :

y² = -8x

Comparing given equation with parabola having equation,

y² = - 4ax

4a = 8

• a = 2

Focus : F(-a,0) = F(-2,0)

Vertex : A(0,0) = A(0,0)

Equation of the directrix : x – a = 0

• x – 2 = 0

• x = 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 :y2 = -8x

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 :
y² = -8x