/*! 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} Q 30. Find the equation of the parabol... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Q 30. (page 643)

Find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand.

Vertex is at4,-2and focus is at6,-2.

Short Answer

Expert verified

The equation of a parabola is

y+22=8x-4.

The points are6,2;6,-6.

The graph of an equation is

Step by step solution

01

Step 1. Given Information.

The given vertex is at4,-2and focus is at6,-2.

02

Step 2. Equation of a parabola.

The vertex is at 4,-2and focus 6,-2both lie on the horizontal line y=-2(the axis of symmetry). The distance a from the vertex to the focus is a=-2.

The parabola opens to the right. The form of a equation is

y-k2=-4ax-h.

where h,k=4,-2and a=-2. Therefore, the equation is

y+22=8x-4.

03

Step 3. Latus rectum.

The two points that determines the latus rectum by letting x=6, so that

y+22=8x-4y+22=82y+22=16y+2=卤4y+2=4,y+2=-4y=2,-6.

The points are6,2and6,-6.

04

Step 4. Graphing Utility.

The graph of a parabola is

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 equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand.

Focus at0,2and its vertex at0,0.

In Problems 31鈥� 42, rotate the axes so that the new equation contains no xy-term. Analyze and graph the new equation. Refer to Problems 21鈥�30 for Problems 31鈥� 40.4x2-4xy+y2-85x-165y=0

In Problems 31鈥� 42, rotate the axes so that the new equation contains no xy-term. Analyze and graph the new equation. Refer to Problems 21鈥�30 for Problems 31鈥� 40.

5x2+6xy+5y2-8=0

In Problems 19鈥�28, find an equation for the hyperbola described. Graph the equation by hand. Center at (0,0); focus at (3,0); vertex at(1,0).

To transform the equation

Ax2+Bxy+Cy2+Dx+Ey+F=0,B鈮�0

into one in x'and y'without an x'y'-term, rotate the axes

through an acute angle 胃that satisfies the equation _______.
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Mechanics 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.