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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Warm-Up: Review What You Know

These problems review skills you have already learned.

How far is the point $(6, 2)$ from the horizontal line $y = -3$ ?

$\sqrt{45}$ , found by applying the distance formula from $(6, 2)$ to the point $(0, -3)$ where the line crosses the $y$ -axis.

$5$ , because the shortest path from a point to a horizontal line is straight down, a change of $2 - (-3)$ units in $y$ only.

$3$ , because the line is $y = -3$ and the distance to a line named by a number is that number.

$\sqrt{85}$ , found by applying the distance formula from $(6, 2)$ to the origin-side point $(-3, 0)$ on the line.