Write an equation of a parabola having focus (0, 5) and directrix y = -5. A) x² = 20y B) y² = 5x C) y² = 20x D) x² = 5y E) y² = -5x

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Quizplus · Accepted Answer

The correct equation of a parabola with focus (0, 5) and directrix y = -5 is $y^2 = 20x$. This is because the vertex is at the midpoint between the focus and directrix, which is at (0, 0), and the distance from the vertex to the focus (or to the directrix) is 5, making the value of $4p = 20$, where $p$ is the distance from the vertex to the focus. Since the parabola opens upwards (focus above the directrix), the correct form is $y^2 = 4px$, which simplifies to $y^2 = 20x$.

Write an Equation of a Parabola Having Focus (0, 5)