x^2 = 12 y equation of the directrix y=-3x^2 = -12 y equation of directrix y= 3y^2 = 12 x Β equation of directrix x=-3y^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 yx^2 = -12 yy^2 = 12 xy^2 = -12 x
For each part the value of directrix will be different.
For xΒ² Β = 12 y
The above equation involves xΒ² , 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:
xΒ² = 4ay Β eq(i)
and our equation in question is: xΒ² = 12y eq(ii)
By putting value of xΒ² 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 xΒ²= 12y is y = -3
For xΒ² Β = -12 y
The above equation involves xΒ² , 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:
xΒ² = -4ay Β eq(i)
and our equation in question is: xΒ² = -12y eq(ii)
By putting value of xΒ² 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 xΒ²= -12y is y = 3
For yΒ² Β = 12 x
The above equation involves yΒ² , 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:
yΒ² = 4ax Β eq(i)
and our equation in question is: yΒ² = 12x eq(ii)
By putting value of yΒ² 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 yΒ²= 12x is x = -3
For yΒ² Β = -12 x
The above equation involves yΒ² , 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:
yΒ² = -4ax Β eq(i)
and our equation in question is: yΒ² = -12x eq(ii)
By putting value of yΒ² 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 yΒ²= -12x is x = 3
