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problems on conics

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This document contains 5 problems identifying different conic sections from their equations. Problem 1 identifies -3x^2 + y + 2 = 0 as a parabola. Problem 2 identifies 2x^2 +3xy - 4y^2 + 2x - 3y + 1 = 0 as a hyperbola. Problem 3 identifies 2x^2 -3y^2 = 0 as a hyperbola. Problem 4 identifies -3x^2 + xy - 2y^2 + 4 = 0 as either an ellipse or circle. Problem 5 identifies x = 0 as a degenerate conic that is a line.

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PROBLEMS ON CONICS
Problem 1.1: Is the following conic a parabola, an ellipse, a circle, or a hyperbola: -3x2 + y + 2 = 0? [Solution] It is a parabola. Problem 1.2: Is the following conic a parabola, an ellipse, a circle, or a hyperbola: 2x2 +3xy - 4y2 + 2x - 3y + 1 = 0? [Solution] It is a hyperbola. Problem 1.3: Is the following conic a parabola, an ellipse, a circle, or a hyperbola: 2x2 -3y2 = 0? [Solution] It is a hyperbola.
Problem 1.4: Is the following conic a parabola, an ellipse, a circle, or a hyperbola: -3x2 + xy - 2y2 + 4 = 0? [Solution] It is an ellipse or a circle. Problem 1.5: Is the following conic a parabola, an ellipse, a circle, or a hyperbola: x = 0? [Solution] It is a degenerate conic. x = 0 is a line.

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problems on conics

  • 2. Problem 1.1: Is the following conic a parabola, an ellipse, a circle, or a hyperbola: -3x2 + y + 2 = 0? [Solution] It is a parabola. Problem 1.2: Is the following conic a parabola, an ellipse, a circle, or a hyperbola: 2x2 +3xy - 4y2 + 2x - 3y + 1 = 0? [Solution] It is a hyperbola. Problem 1.3: Is the following conic a parabola, an ellipse, a circle, or a hyperbola: 2x2 -3y2 = 0? [Solution] It is a hyperbola.
  • 3. Problem 1.4: Is the following conic a parabola, an ellipse, a circle, or a hyperbola: -3x2 + xy - 2y2 + 4 = 0? [Solution] It is an ellipse or a circle. Problem 1.5: Is the following conic a parabola, an ellipse, a circle, or a hyperbola: x = 0? [Solution] It is a degenerate conic. x = 0 is a line.