Intermediate Algebra

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



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.



The given equation for hyperbola is,



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


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,


To find y-intercepts,

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


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



Consider the given hyperbola equation,


Substitute 0 for y in equation (1),


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),


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,


Substitute 1 for x in equation (2),


Plot the point on graph (1,±172)

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