/*! 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. 12 Find the rectangular equation of... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Q. 12 (page 701)

Find the rectangular equation of the curve.

x=5tant,y=sec2t,-蟺2<t<蟺2

Short Answer

Expert verified

The required equation isx2=25(y-1)

Step by step solution

01

Step 1. Given Information

The given parametric equations arex=5tant,y=5sec2t

02

Step 2. Explanation

We will use the pythagorean identity, sec2t-tan2t=1to find the required equation.

Let us obtain the value of tantandsectin terms of xandyfrom the given parametric equations.

localid="1648802898629" role="math" 5tant=x鈬�tant=x5y=sec2t鈬�sect=卤y

Substitute the values in the pythagorean theorem,

卤y2-x52=1y-x252=1x2=25y-1

Thus, the obtained equation is of parabola whose focal distance is localid="1648803390459" a=254and whose vertex is at the point with coordinates 0,1

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 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� 40.13x2-63xy+7y2-16=0

Answer Problem using the figure.

If a = 4, then the equation of the directrix is______ .

In Problems 27鈥�34, find two different parametric equations for each rectangular equationy=x3

Transform the equation r=6cos(胃)from polar coordinate to rectangular coordinate.

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
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Statistics

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.