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 = 12x

Philoid · Accepted Answer

Given equation : y² = 12x

Comparing given equation with parabola having equation,

y² = 4ax

4a = 12

• a =3

Focus : F(a,0) = F(3,0)

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

Equation of the directrix : x+a=0

• x+3=0

• x = -3

Lenth of latusrectum : 4a = 4.(3) = 12

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 = 12x

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 = 12x