/*! 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 54 Find the standard form of the eq... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 54

Find the standard form of the equation of the parabola with the given characteristics. Vertex: \((1,2) ;\) directrix: \(y=-1\)

Short Answer

Expert verified
The standard form of the equation of the parabola with the given characteristics is \(y = 1/12(x - 1)^2 + 2\).

Step by step solution

01

Find a

The formula for a is 1/(4d), where d is the distance between the vertex and the directrix. Since the vertex is (1,2) and the directrix is y=-1, the distance d is 2 -(-1) = 3. Therefore, \(a = 1/(4*3) = 1/12\).
02

Write the standard form of the parabola

Now that we have the value for a, we can substitute it into the standard form of a parabola. Since the parabola opens upwards (because a > 0), and the vertex is (1,2), the equation of the parabola is \(y = 1/12(x - 1)^2 + 2\).

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

In Exercises \(91-116\), convert the polar equation to rectangular form. $$\theta=2 \pi / 3$$

Write a short paragraph explaining why parametric equations are useful.

Find the distance between the point and the line. Point \((2,1)\) Line \(y=x+2\)

Find the distance between the point and the line. Point \((1,-3)\) Line \(4 x-3 y=-7\)

In Exercises \(129-132,\) determine whether the statement is true or false. Justify your answer. If \(\left(r_{1}, \theta_{1}\right)\) and \(\left(r_{2}, \theta_{2}\right)\) represent the same point in the polar coordinate system, then \(\left|r_{1}\right|=\left|r_{2}\right|\).
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

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.