   Chapter 10.1, Problem 57E

Chapter
Section
Textbook Problem

Using an Equation Consider the equation 9 x 2 + 4 y 2 − 36 x − 24 y − 36 = 0 .(a) Classify the graph of the equation as a circle, aparabola, an ellipse, or a hyperbola.(b) Change the 4 y 2 − term in the equation to − 4 y 2 .Classify the graph of the new equation.(c) Change the 9 x 2 − term in the original equation to 4 x 2 .Classify the graph of the new equation.(d) Describe one way you could change the originalequation so that its graph is a parabola.

a)

To determine

To calculate: The equation 9x2+4y236x24y36=0 as a circle, parabola, ellipse, and hyperbola.

Explanation

Given:

The equation is;

9x2+4y236x24y36=0

Formula used:

The standard equation of ellipse,

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

Calculation:

Complete the square on left hand side;

9x2+4y236x24y36=09x236x+3636+4y224y+363636=

b)

To determine

To calculate: The equation 9x24y236x24y36=0 as a circle, parabola, ellipse, and hyperbola.

c)

To determine

To calculate: The equation 4x2+4y236x24y36=0 as a circle, parabola, ellipse, and hyperbola.

d)

To determine
A way in which we can make the equation 9x2+4y236x24y36=0.Solution: Removal of either of the quadratic terms

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