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This algebra 2 math tutorial from NutshellMath offers targeted math homework help on identifying equations of conics. The instruction in this tutorial is focused on problems 3, 8-11 and 29-44 on pages 628 and 629 in the Algebra 2: Applications, Equations, Graphs text from McDougal Littell. Conic sections are a special class of curves, including parabolas, hyperbolas, circles and ellipses, which arise from the intersection of a cone and a plane. When graphed on a coordinate plane, these curves are all represented by quadratic equations with two variables. In fact, all quadratic equations with two variables graph as conics on the coordinate plane.
This tutorial introduces the general form for a second-degree equation. This form is the general form of a two-variable quadratic that graphs as a conic. It is possible use the general form of any quadratic equation to determine which type of conic section in which the equation will graph. To classify a conic in this way it is first necessary to rearrange it in general second-order form, and then find the discriminant. The discriminant is the square of the coefficient of the xy term less four times the product of the two quadratic coefficients. If the discriminant is less than zero, then the conic will graph to a circle or an ellipse. For the conic to be a circle, the coefficient of the xy term must be zero, and the coefficients of the quadratic terms must be the same. Otherwise, the conic is an ellipse. Equations with discriminants equal to zero graph as parabolas, and equations with discriminants greater than zero graph as hyperbolas.
To quickly classify conics, first rearrange the equation into standard form and determine the discriminant. From the discriminant it is possible to determine which type of conic the equation represents using the relationships described above. Using this method it is possible to quickly classify conics when given a quadratic equation in two variables. Examples in this tutorial will reinforce this skill and help with homework problems involving conics and quadratic equations.
This algebra 2 math tutorial from NutshellMath offers targeted math homework help on identifying equations of conics. The instruction in this tutorial is focused on problems 3, 8-11 and 29-44 on pages 628 and 629 in the Algebra 2: Applications, Equations, Graphs text from McDougal Littell. Conic sections are a special class of curves, including parabolas, hyperbolas, circles and ellipses, which arise from the intersection of a cone and a plane. When graphed on a coordinate plane, these curves are all represented by quadratic equations with two variables. In fact, all quadratic equations with two variables graph as conics on the coordinate plane.
This tutorial introduces the general form for a second-degree equation. This form is the general form of a two-variable quadratic that graphs as a conic. It is possible use the general form of any quadratic equation to determine which type of conic section in which the equation will graph. To classify a conic in this way it is first necessary to rearrange it in general second-order form, and then find the discriminant. The discriminant is the square of the coefficient of the xy term less four times the product of the two quadratic coefficients. If the discriminant is less than zero, then the conic will graph to a circle or an ellipse. For the conic to be a circle, the coefficient of the xy term must be zero, and the coefficients of the quadratic terms must be the same. Otherwise, the conic is an ellipse. Equations with discriminants equal to zero graph as parabolas, and equations with discriminants greater than zero graph as hyperbolas.
To quickly classify conics, first rearrange the equation into standard form and determine the discriminant. From the discriminant it is possible to determine which type of conic the equation represents using the relationships described above. Using this method it is possible to quickly classify conics when given a quadratic equation in two variables. Examples in this tutorial will reinforce this skill and help with homework problems involving conics and quadratic equations.