55-64 ■ Find the Equation of the Conic Find an equation for the conic section with the given properties.
The parabola with focus and directrix .
An equation for the parabola with focus and directrix .
The focus and directrix of the parabola are and respectively.
Take a point on the parabola, Then the perpendicular distance from point to the directrix is equal to the distance between point and focus, because the eccentricity is equal to one in case of parabola.
Consider an arbitrary point on the parabola. Its distance from the focus is given as follows,
Let be the perpendicular distance between point and directrix, .
Equate distances and , and square both sides
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