Back to Derive parabola equation — Problem 2 · 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

What is the directrix of the parabola $x^2 = 16y$ ?

$y = 4$ , placing the directrix on the same side of the vertex as the focus.

$x = -4$ , treating the parabola as opening sideways because the equation begins with $x^2$ .

$y = -16$ , reading the directrix straight off the coefficient $16$ without solving $4p = 16$ .

$y = -4$ , since $4p = 16$ gives $p = 4$ and the directrix of an upward parabola is $y = -p$ .