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Ellipses (page 7) General form is Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 where A ≠ C and A and C are same sign x h Standard form: Major Axis: a 2 2 y k b 2 2 The variable with the longest axis Center: h, k ‘a’: Distance in the x direction ‘b’: Distance in the y direction Vertices: Covertices: 1 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. 2 y 2 ( x 1) 1) Graph the ellipse 1 9 36 2 6 4 2 Length of major axis: -5 5 Length of minor axis: -2 Horizontal or vertical: -4 -6 2) Graph the ellipse 16x2 + 32x = -y2 6 4 2 -5 5 -2 -4 -6 3) Graph the ellipse 4x2 + 9y2 – 16x + 54y + 61 = 0 6 4 2 -5 5 -2 -4 -6