Answer:
- 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
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