Tilted Conics 1.Use the discriminant to classify conics. 2.Rotate the coordinate axes to eliminate the xy term in equations of conics. 1

Classifying Conics Non-Degenerate tiltedDegenerate +Hyperbola2 intersecting lines 0Parabola2 || lines -EllipseA point For Ax 2 +Bxy+Cy 2 +Dx+Ey+F=0, the xy tem gives a tilt to a hyperbola, ellipse, or parabola. 2

Example b 2 -4ac Type of Conic x 2 +2xy+y 2 -6x+7y=17 x 2 +2xy+5y 2 -6x+7y=17 x 2 +12xy+5y 2 -6x+7y=17 3

Sketching a Tilted Conic 4

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Rotation of Axes How do you eliminate the xy term from the general equation to help classify and sketch? 10

Rotation Formulas 11

Find the angle of rotation needed to eliminate the xy term 12

xy+2=0 13

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Practice Day Open Notebook Quiz 17