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The image shows a parabola with focus
Parabola with focus at negative 2 comma 2 and directrix y equals 0, the x axis. Point A is 2 comma 5, point B is negative 8 comma 10, point C is negative x comma y and all points are on the parabola.
Without using the Pythagorean Theorem, find the distance from each plotted point to the parabola’s focus. Explain your reasoning.
The image shows a parabola with focus
The parabola in the image consists of all the points that are the same distance from the point
Suppose we want to write an equation for the parabola—that is, an equation that says a given point
Parabola with a focus of 1 comma 4 and directrix y equals 0. All points on parabola are same distance from point 1 comma 4. The point x comma y is on the parabola. Triangle consists of sides labeled y for the hypotenuse, x minus 1 and y minus 4. Parabola contains point 1 comma 2.
The distance from
Substitute the expressions for the side lengths into the Pythagorean Theorem to get an equation defining the parabola.
To get the equation looking more familiar, rewrite it in vertex form, or
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