Chapter 2: Q. 61 (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.
$x^{2} - 3 y^{2} = 16$

Short Answer

Expert verified

The equation for $y$ is $y = \sqrt{\frac{x^{2} - 16}{3}}$

Step by step solution

Step 1. Given Information

The given equation is $x^{2} - 3 y^{2} = 16$

Step 2. Solve for y

$x^{2} - 3 y^{2} = 16 3 y^{2} = x^{2} - 16 y^{2} = \frac{x^{2} - 16}{3} y = \sqrt{\frac{x^{2} - 16}{3}}$

Step 3. Graph of the Equation

We obtained $y = \pm \sqrt{\frac{x^{2} - 16}{3}}$

The graph of hyperbola is shown in the figure

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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.
$x^{2} - 3 y^{2} = 16$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solve for y

Step 3. Graph of the Equation

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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.x2-3y2=16

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

Geometry

Statistics

Pure Maths

Calculus

Theoretical and Mathematical Physics

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.
$x^{2} - 3 y^{2} = 16$