   Chapter 12.4, Problem 55E ### 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

# 47-58 Graphing Shifted Conics Complete the square to determine 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 the lengths of the major and minor axes. If it is parabola, find the vertex, focus, and directrix. If it is 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 + 16 = 4 ( y 2 + 2 x ) .

To determine

The graph of the equation and its characteristics.

Explanation

Given:

The given equation is 4x2+16=4(y2+2x)

Approach:

Write the equation of line in intercept form.

xa+yb=1

Here, a is the x-intercept and b is the y-intercept.

Calculation:

Consider the given equation,

4x2+16=4(y2+2x)

Now complete the square as shown below,

x28x+16=4y2(x4)24y2=0(x4)2=4y2x4=±2y

Further solve the above equation.

x4=2yx2y=4 …… (1)

Also,

x4=2yx+2y=4 …… (2)

These are two equations of straight lines and both are intersecting.

Consider the equation (1).

x2y=4x4+y(2)=1

The two coordinates which lie on this line are,

(4,0) and (0,2)

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