Chapter 2: Q. 62 (page 210)

For each of the equations in Exercises 59–62, y is defined as an implicit function of x. Solve for y, and use what you find to sketch a graph of the equation.
$4 y^{2} - x^{2} + 25 = 0$

Short Answer

Expert verified

The equation of $y$ is $y = \frac{\sqrt{x^{2} - 25}}{2}$

Step by step solution

Step 1. Given Information

The given equation is $4 y^{2} - x^{2} + 25 = 0$

Step 2. Solve for y

$4 y^{2} = x^{2} - 25 y^{2} = \frac{x^{2} - 25}{4} y = \frac{\sqrt{x^{2} - 25}}{2}$

Step 3. Graph of the Equation

We obtained $y = \frac{\pm \sqrt{x^{2} - 25}}{2}$

The graph of hyperbola 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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

For each of the equations in Exercises 59–62, y is defined as an implicit function of x. Solve for y, and use what you find to sketch a graph of the equation.
$4 y^{2} - x^{2} + 25 = 0$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solve for y

Step 3. Graph of the Equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Applied Mathematics

Mechanics Maths

Logic and Functions

Geometry

Probability and Statistics

Study anywhere. Anytime. Across all devices.

For each of the equations in Exercises 59–62, y is defined as an implicit function of x. Solve for y, and use what you find to sketch a graph of the equation.4y2-x2+25=0

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solve for y

Step 3. Graph of the Equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Applied Mathematics

Mechanics Maths

Logic and Functions

Geometry

Probability and Statistics

Study anywhere. Anytime. Across all devices.

For each of the equations in Exercises 59–62, y is defined as an implicit function of x. Solve for y, and use what you find to sketch a graph of the equation.
$4 y^{2} - x^{2} + 25 = 0$