Find the equation of the directrix of the parabola x2=+ / - 12y and y2=+ / - 12x

x^2 = 12 y equation of the directrix y=-3 x^2 = - 12 y equation of directrix y = 3 y^2 = 12 x equation of directrix x=-3 y^2 = - 12 x equation of directrix x = 3

Step-by-step explanation:

To find the equation of directrix of the parabola, we need to identify the axis of the parabola i. e, parabola lies in x-axis or y-axis.

We have 4 parts in this question i. e.

x^2 = 12 y x^2 = - 12 y y^2 = 12 x y^2 = - 12 x

For each part the value of directrix will be different.

For x² = 12 y

The above equation involves x², the axis will be y-axis

The formula used to find directrix will be: y = - a

So, we need to find the value of a.

The general form of equation for y-axis parabola having positive co-efficient is:

x² = 4ay eq (i)

and our equation in question is: x² = 12y eq (ii)

By putting value of x² of eq (i) into eq (ii) and solving:

4ay = 12y

a = 12y/4y

a = 3

Putting value of a in equation of directrix: y = - a = > y = - 3

The equation of the directrix of the parabola x² = 12y is y = - 3

For x² = - 12 y

The above equation involves x², the axis will be y-axis

The formula used to find directrix will be: y = a

So, we need to find the value of a.

The general form of equation for y-axis parabola having negative co-efficient is:

x² = - 4ay eq (i)

and our equation in question is: x² = - 12y eq (ii)

By putting value of x² of eq (i) into eq (ii) and solving:

-4ay = - 12y

a = - 12y/-4y

a = 3

Putting value of a in equation of directrix: y = a = > y = 3

The equation of the directrix of the parabola x² = - 12y is y = 3

For y² = 12 x

The above equation involves y², the axis will be x-axis

The formula used to find directrix will be: x = - a

So, we need to find the value of a.

The general form of equation for x-axis parabola having positive co-efficient is:

y² = 4ax eq (i)

and our equation in question is: y² = 12x eq (ii)

By putting value of y² of eq (i) into eq (ii) and solving:

4ax = 12x

a = 12x/4x

a = 3

Putting value of a in equation of directrix: x = - a = > x = - 3

The equation of the directrix of the parabola y² = 12x is x = - 3

For y² = - 12 x

The above equation involves y², the axis will be x-axis

The formula used to find directrix will be: x = a

So, we need to find the value of a.

The general form of equation for x-axis parabola having negative co-efficient is:

y² = - 4ax eq (i)

and our equation in question is: y² = - 12x eq (ii)

By putting value of y² of eq (i) into eq (ii) and solving:

-4ax = - 12x

a = - 12x/-4x

a = 3

Putting value of a in equation of directrix: x = a = > x = 3

The equation of the directrix of the parabola y² = - 12x is x = 3