CCGPS AG 6.1.2 Example 2
Derive the standard equation of the parabola with focus and directrix from the definition of a parabola. Then write the equation by substituting the vertex coordinates and the value of directly into the standard form.
- To derive the equation, begin by plotting the focus. Label it . Graph the directrix and label it . Sketch the parabola. Label the vertex .
- Let be any point on the parabola.
- Apply the definition of a parabola to derive the standard equation using the distance formula.
- Write the equation using standard form.
- Use the results found in step 4 to write the equation.