SOLUTION: Find the focus, vertex, length of latus rectum,and the equation of directrix of the parabola y^2

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Question 1119528: Find the focus, vertex, length of latus rectum,and the equation of directrix of the parabola y^2 - 10x = 0
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) (Show Source):
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Vertex is (0,0).

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Focus is ( 2.5, 0 ).

Directrix is .
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Answer by greenestamps(13200) (Show Source):
You can put this solution on YOUR website!

The equation has a y^2 term, so the parabola opens right or left. Vertex form for the equation of a parabola that opens right or left is

where the vertex is (h,k) and p is the directed distance from the directrix to the vertex and from the vertex to the focus.

Note with this form of the equation, the length of the latus rectum (perpendicular to the axis of symmetry and through the focus) is |4p|.

Put the given equation in that form:

This is in vertex form. The vertex is (0,0); p = 10/4 = 2.5.

vertex: (0,0)
focus: p = 2.5 right of the vertex, at (2.5,0)
directrix: p = 2.5 left of the vertex; x = -2.5
length of latus rectum: 4p = 10

SOLUTION: Find the focus, vertex, length of latus rectum,and the equation of directrix of the parabola y^2 - 10x = 0