Identify the equation without applying a rotation of axes. $3x^2 - 3xy + 6y^2 - 18 = 0$ Choose the correct answer below. A. ellipse or circle B. hyperbola C. parabola
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Step 1: To identify the type of conic section without applying a rotation of axes, we can look at the coefficients of the x^2, xy, and y^2 terms in the equation. Show more…
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Rotate the axes so that the new equation contains no xy-term. Discuss and graph the new equation. x^2 + 10xy + y^2 - 3 = 0 Choose the conic that matches this equation: A. Ellipse B. Parabola C. The equation does not represent a conic. D. Hyperbola Enter the location of the center of the conic. (h, k) = ( , ) Enter the angle of rotation that eliminates the xy-term of the equation of the conic. Choose the correct transverse axis of the rotated conic. A. x' B. y' Enter the coordinates of the vertices of the conic in the x'-y' plane. (± , ) (Simplify your answer. Rationalize all denominators.)
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Graphing a Rotated Conic (a) Use the discriminant to determine whether the graph of the equation is a parabola, an ellipse, or a hyperbola. (b) Use a rotation of axes to eliminate the xy-term. (c) Sketch the graph. $$ 2 \sqrt{3} x^{2}-6 x y+\sqrt{3} x+3 y=0 $$
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