SOLUTION: Find an equation of the parabola in standard form having the given properties. Draw a sketch of the parabola ( make sure to emphasize all of the properties of the parabola) A. v

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find an equation of the parabola in standard form having the given properties. Draw a sketch of the parabola ( make sure to emphasize all of the properties of the parabola) A. v      Log On


   

Question 1168614: Find an equation of the parabola in standard form having the given properties. Draw a sketch of the parabola ( make sure to emphasize all of the properties of the parabola)
A. vertex at (2,4), focus at (-3,4)
B. vertex at origin, opens upward, length of latus rectum is 4 units
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
A quick sketch and simple computation shows that directrix is x=7, or all points in the plane, (7,y).

Distance from (x,y) to (-3,4) is equal to distance from (x,y) to (7,y).

Setup using the Distance Formula definition for parabola and start with
%28x%2B3%29%5E2%2B%28y-4%29%5E2=%28x-7%29%5E2%2B%28y-y%29%5E2

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Upon doing the algebra steps an equation found highlight%28%28y-4%29%5E2=-20%28x-2%29%29.