Back to Derive parabola equation — Problem 6 · Task Set 31

Exercises: Derive the Equation of a Parabola Given Focus and Directrix

Show your work for each problem. Unless a problem says otherwise, assume the axis of symmetry is horizontal or vertical, and give equations in standard form.

Grade 10·23 problems·~35 min·Common Core Math - HS Geometry·standard·hsg-gpe-a-2

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Fluency Practice

The parabola $y = 2x^2$ has vertex at the origin. What is its focal length $p$ ?

$p = 2$ , reading the focal length directly from the coefficient of $x^2$ .

$p = 8$ , computing $4a$ with $a = 2$ instead of dividing.

$p = \frac{1}{8}$ , since $a = \frac{1}{4p}$ means $p = \frac{1}{4a} = \frac{1}{4(2)}$ .

$p = \frac{1}{2}$ , taking the reciprocal of the coefficient $a = 2$ without the factor of $4$ .