   Chapter 12.4, Problem 54E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# SKILLS47-58 ■ Graphing Shifted Conics Complete the square to deter-mine whether the graph of the equation is an ellipse, a parabola, a hyperbola, or a degenerate conic. If the graph is an ellipse, find the center, foci, vertices, and lengths of the major and minor axes. If it is a parabola, find the vertex, focus, and directrix. If it is a hyperbola, find the center, foci, vertices, and asymptotes. Then sketch the graph of the equation. If the equation has no graph, explain why. 4 x 2 − 4 x − 8 y + 9 = 0

To determine

The conic and its characteristics. Also, graph the conic.

Explanation

Given:

The given equation is,

4x24x8y+9=0

Approach:

The general equation of a parabola is,

x2=4py

Expression to find vertex is,

V(0,0)

Expression to find Focus is,

F(0,p)

Expression to find directrix is,

y=p

The parabola opens upward if p>0 or downward if p<0.

Calculation:

Consider the given equation,

4x24x8y+9=0

Now complete the square as shown below,

4x24x8y+9=04x24x+118y+9=0(2x1)28y=8(2x1)28+y=1

Further solve,

4(x12)28+y1=14(x12)2=8y8(

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