Ellipses (page 7) General form is Ax 2 + Bxy + Cy 2 + Dx + Ey + F = 0 where A ≠ C and A and C are same sign.

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Ellipses (page 7) General form is Ax 2 + Bxy + Cy 2 + Dx + Ey + F = 0 where A ≠ C and A and C are same sign

Standard form: Major Axis: Center: ‘a’: ‘b’: Vertices: Covertices: The variable with the longest axis Distance in the x direction Distance in the y direction Endpoints of the major axis Endpoints of the minor axis

Ex. Write the equation of the ellipse. 1)Find the center 2)Find a and b 3)Simplify

1) Write the equation of the ellipse.

2) Write the equation of the ellipse.

To graph, we may need to put the equation into standard form.  This may require us to complete the square for the x terms and the y terms.  Notice that standard form has everything equal to 1.

1) Graph the ellipse Length of major axis: Length of minor axis: Horizontal or vertical:

2) Graph the ellipse 16x x = -y 2

3) Graph the ellipse 4x 2 + 9y 2 – 16x + 54y + 61 = 0