   Chapter 8.4, Problem 10PS ### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
ISBN: 9781285195728

#### Solutions

Chapter
Section ### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
ISBN: 9781285195728
Textbook Problem

# For Problems 7 − 18 , graph each hyperbola. (Objective 1) 4 y 2 − x 2 = 16

To determine

To plot:

The graph for given equation of hyperbola.

Explanation

Given:

The given equation for hyperbola is,

4y2x2=16

Approach:

The formula of hyperbola that is symmetric with respect to the origin is as follows,

Ax2By2=C

Here, C is constant term and A, B and C are nonzero real numbers.

To find the x-intercept,

Substitute 0 for y in the equation of hyperbola and solve for x as follows,

Ax2B(0)2=C

To find y-intercepts,

Substitute 0 for x in the equation of hyperbola and solve for y as follows,

A(0)2By2=C

To find the equation for the asymptotes replace the constant term of Ax2By2=C with 0 and solve for y as follows,

Ax2By2=0

Calculation:

Consider the given hyperbola equation,

4y2x2=16(1)

Substitute 0 for y in equation (1),

4(0)2x2=16x2=16x2=16

Since, x2=16 has no real number solution. Hence there is no real x-intercepts for the given hyperbola

Substitute 0 for x in equation (1),

4y2(0)2=164y2=16y2=164y=±2

Therefore the y-intercepts points (0,2) and (0,2) are on the graph.

Consider equation (1) and solve for y yields and set up a table as follows,

4y2x2=164y2=16+x2y2=x2+164y=±12x2+16(2)

Substitute 1 for x in equation (2),

y=±12(1)2+16=±172

Plot the point on graph (1,±172)

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