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Focal Diameter of Parabola

by Zachary
(CA, USA)











































Find the focal diameter of the parabola

x = -2y squared

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May 11, 2012
Focal Diameter of Parabola
by: Staff


Question:

by Zachary
(CA, USA)

Find the focal diameter of the parabola

x = -2y squared


Answer:

The general equation of a PARABOLA with a HORIZONTAL AXIS of symmetry is:

4px = y²

x = y²/(4p)



Vertex: (0, 0)

Focus: (p, 0)
[the focus must lie on this axis of symmetry]

Directrix: x = -p
[the directrix must cross through this axis of symmetry]

Focal diameter: │4p│
[The focal diameter is the length of the line segment that is perpendicular to the x axis (in this case), runs through the focus, and has its end points on the parabola.]

Parabola Opens: to the right if p > 0, to the left if p < 0

---------------------------------------------

x = -2y²

since x = y²/(4p)

then,

-2 = 1/(4p)

p = 1/[4*(-2)]

p = -1/8

(p is the distance between the vertex of the parabola and the focus)

Vertex: (0, 0)

Focus: (p, 0)

Therefore

Focus = (-1/8, 0)

The x coordinate of the directrix is also the distance “p” from the vertex, but in the opposite direction.

Directrix: x = -p

x = -(-1/8)

x = 1/8

Directrix: x = 1/8

Focal diameter: │4p│

= │4 * (-1/8)│

= │(-4/8)│
= │(-1/2)│


= ½


>>> the final answer is:

the focal diameter of the parabola = ½





Thanks for writing.

Staff
www.solving-math-problems.com




Apr 13, 2017
x=-3y^2 NEW
by: Anonymous

x=-3y^2

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