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Chapter 7: Problem 22

Find the standard form of the equation of each parabola satisfying the given conditions. Focus: \((0,20) ;\) Directrix: \(y=-20\)

Short Answer

Expert verified
The standard form of the equation of the parabola is \(y = 5x^2\).

Step by step solution

01

Identify the vertex

Since the parabola is symmetric with respect to the x-axis and the focus and directrix are mirror images in relation to the x-axis, the vertex of the parabola is at the origin (0,0).
02

Determine the opening direction

Since the focus (0,20) is above the vertex, the parabola opens upwards.
03

Find the value of a

The distance from the vertex to the focus or to the directrix is |4a|. Hence, |4a| = 20, which means a = 5.
04

Formulate the standard equation

For a parabola opening upwards, the standard form is \(y = ax^2\). Thus, replacing \(a\) with 5 yields the standard form of the parabola: \(y = 5x^2\).

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