EMAT 6680

Assignment 2

Stephanie K. Lewis

10. Graph x^{2 }+ y^{2} = 9

On, the same axes, graph x^{2 }+ xy + y^{2} = 9

- If
**a**and**b**are equal, then the graph will be a circle.Let a = 2 and b = 2. Then the graph of 2x

^{2}+ 2y^{2}= 9 (in purple) and the graph of 2x^{2}+ (2)(2) + 2y^{2}= 9 (in red) are illustrated below. - If
**a**,**b**, and**c**have the same signs, and**a**and**b**are unequal, then the graph will be an ellipse.Let a = 2 and b = 4. Then the graphs of 2x

^{2}+ 4y^{2}= 9 (in purple), and 2x^{2}+ (2)( 4) + 4y^{2}= 9 (in red) are illustrated below.3. If

**a**and**b**have opposite signs, then the graph will be a hyperbola.

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__Describe the new graph__.

The new graph is an ellipse with x-intercepts at (-3,0) and (3,0) and y-intercepts at (0,3) and (0, -3). The lines of symmetry appear to be the lines y = x and y = -x

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__Try different coefficients for the xy term. What kinds of graphs do
you generate__?

If we let **a** represent the x term coefficient, **b** represent
the y term coefficient, and **c** represent the constant, then the following
observations can be made. In general,