SOLUTION: What is the vertex, directrix, principal axis, graph, and the standard form of the following. If your given with endpoints of the Latus Rectum by (-1,6) and (-1,-2) and p < 0.

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: What is the vertex, directrix, principal axis, graph, and the standard form of the following. If your given with endpoints of the Latus Rectum by (-1,6) and (-1,-2) and p < 0.      Log On


   

Question 1042193: What is the vertex, directrix, principal axis, graph, and the standard form of the following. If your given with endpoints of the Latus Rectum by (-1,6) and (-1,-2) and p < 0.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Endpoints to the Latus Rectum tells you the focus. p<0 tells you the sign of the leading coefficient factor, being negative and therefore which side of the parabola to expect the focus. Otherwise, your given information is SEEMS incomplete, but keep going...

x coordinate for the focus is -1.
y coordinate for the focus is %286%2B%28-2%29%29%2F2=4%2F2=2.
Focus Point is (-1,2).

Expect Latus Rectum to be perpendicular to axis of symmetry. The focus in on the symmetry axis; so this axis is y=2.

Basic Model for standard form equation is x=a%28y-2%29%5E2%2Bh for VERTEX (h,k) and you know that a%3C0, but you do not yet know nor have a directrix known. Knowing p and a both less than 0, this parabola will open to the left. Vertex and directrix will be located to the right of the focus.

At best, you can use the two given points:
system%28k=2%2C+h=stillUnknown%29;
x=a%28y-2%29%5E2%2Bh
and then with the two given points (endpoints to Latus Recturm):
system%28-1=a%286-2%29%5E2%2Bh%2C-1=a%28-2-2%29%5E2%2Bh%29
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SIMPLIFY these two equations, and find the values for a and h.


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You may still want some help finding value for p, finding the diredctrix, and then making the graph.