/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 22 Find the standard form of the eq... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

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: \(y = 5x^2\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Find the standard form of the equation of each ellipse satisfying the given conditions. $$\text { Foci: }(-2,0),(2,0) ; \text { vertices: }(-6,0),(6,0)$$

Use a graphing utility to graph the parabolas.Write the given equation as a quadratic equation in \(y\) and use the quadratic formula to solve for \(y .\) Enter each of the equations to produce the complete graph. $$y^{2}+2 y-6 x+13=0$$

Find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola. $$ (y-1)^{2}=-8 x $$

In Exercises \(1-18,\) graph each ellipse and locate the foci. $$25 x^{2}+4 y^{2}=100$$

What is a hyperbola?
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.