   Chapter 10.1, Problem 51E

Chapter
Section
Textbook Problem

# Classifying the Graph of an Equation In Exercises 51–58, classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. x 2 + 4 y 2 − 6 x + 16 y + 21 = 0

To determine

Whether the graph of the equation x2+4y26x+16y+21=0 is a circle, a parabola, an ellipse or a hyperbola.

Explanation

Given:

The provided equation is:

x2+4y26x+16y+21=0.

Formula used:

The standard equation of an ellipse centered at (h,k) with major and minor axes a and b is:

(xh)2a2+(yk)2b2=1

Calculation:

Consider the provided equation:

x2+4y26x+16y+21=0

Now, rewrite the equation with the help of completion of squares as:

(x26x+9)+4(y2+4y+4

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