SOLUTION: Find the focus and directrix of each parabola with the given equation. a). x^=4y b). y^=-4x

Question 481497: Find the focus and directrix of each parabola with the given equation.
a). x^=4y

b). y^=-4x
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Find the focus and directrix of each parabola with the given equation.
a). x^=4y
b). y^=-4x
**
a). x^2=4y
This is an equation of a parabola with a vertical axis of symmetry.
Its standard form: (x-h)^2=4p(y-k), with (h,k) being the (x,y) coordinates of the vertex.
For given equation:
parabola opens upwards
Vertex(0,0)
4p=4
p=1
Focus:(0,1)
Directrix: y=-1
see the graph below as a visual check on the answers:
..
y=�x^2/4

..
b). y^2=-4x
This is an equation of a parabola with a horizontal axis of symmetry.
Its standard form: (y-k)^2=4p(x-h), with (h,k) being the (x,y) coordinates of the vertex.
For given equation:
parabola opens leftward
Vertex(0,0)
4p=4
p=1
Focus:(-1,0)
Directrix: x=1
see the graph below as a visual check on the answers:
..
y=�(-4x)^.5

..
RELATED QUESTIONS
Find the vertex, focus, and directrix of the parabola given by the equation x^2 + 4x + 4y (answered by KMST)

find the vertex, focus, and directrix of the parabola given by each equation. Sketch the... (answered by josgarithmetic)

Find the vertex, focus and directrix of the parabola given by each equation. Sketch the... (answered by josgarithmetic)

FIND THE EQUATION OF THE PARABOLA WITH THE GIVEN FOCUS AND DIRECTRIX. focus (-4,5)... (answered by Fombitz)

find the equation of the parabola with the given focus and directrix. focus... (answered by josgarithmetic,greenestamps)

18. Write an equation of a parabola with the given focus and directrix. Focus-(0,3),... (answered by ewatrrr)

the equation of a parabola with the given focus and directrix F(0,-5),... (answered by lwsshak3)

Find the vertex, focus, and directrix of the parabola with equation... (answered by Edwin McCravy)

Find the focus and directrix of the parabola with the given equation. Then graph the... (answered by lwsshak3)