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- https://math.libretexts.org/Courses/Coastline_College/Math_C097%3A_Support_for_Precalculus_Corequisite%3A_MATH_C170/1.05%3A_Exponential_and_Logarithmic_Functions/1.5.09%3A_Trigonometry_Preview_-_CirclesIf we were to expand the equation in the previous example and gather up like terms, instead of the easily recognizable \((x+2)^2 + (y-1)^2 = 4\), we'd be contending with \(x^2 + 4x + y^2 - 2y + 1 = 0....If we were to expand the equation in the previous example and gather up like terms, instead of the easily recognizable \((x+2)^2 + (y-1)^2 = 4\), we'd be contending with \(x^2 + 4x + y^2 - 2y + 1 = 0.\) If we're given such an equation, we can complete the square to rewrite the equation in standard form for a circle. The diameter of the circle is the distance between the given points, so we know that half of the distance is the radius.
- https://math.libretexts.org/Courses/Prince_Georges_Community_College/MAT_1350%3A_Precalculus_Part_I/02%3A_Equations_and_Inequalities/2.08%3A_CirclesA circle is the set of points in a plane that lie a fixed distance, called the radius, from any point, called the center. The diameter is the length of a line segment passing through the center whose ...A circle is the set of points in a plane that lie a fixed distance, called the radius, from any point, called the center. The diameter is the length of a line segment passing through the center whose endpoints are on the circle. In addition, a circle can be formed by the intersection of a cone and a plane that is perpendicular to the axis of the cone.
- https://math.libretexts.org/Courses/Coastline_College/Math_C120%3A_Trigonometry_(Tran)/04%3A_Further_Applications_of_Trigonometry/4.05%3A_Polar_Coordinates_-_Graphspolar equation describes a relationship between rr and θ on a polar grid. It is easier to graph polar equations if we can test the equations for symmetry. There are three symmetry tests that indic...polar equation describes a relationship between rr and θ on a polar grid. It is easier to graph polar equations if we can test the equations for symmetry. There are three symmetry tests that indicate whether the graph of a polar equation will exhibit symmetry. If an equation fails a symmetry test, the graph may or may not exhibit symmetry.
- https://math.libretexts.org/Courses/Chabot_College/Math_in_Society_(Zhang)/02%3A_Geometry/2.02%3A_Perimeter_Circumference_and_AreaQuadrilaterals are a special type of polygon. As with triangles and other polygons, quadrilaterals have special properties and can be classified by characteristics of their angles and sides. Understan...Quadrilaterals are a special type of polygon. As with triangles and other polygons, quadrilaterals have special properties and can be classified by characteristics of their angles and sides. Understanding the properties of different quadrilaterals can help you in solving problems that involve this type of polygon.
- https://math.libretexts.org/Bookshelves/Algebra/Advanced_Algebra/08%3A_Conic_Sections/8.02%3A_CirclesA circle is the set of points in a plane that lie a fixed distance, called the radius, from any point, called the center. The diameter is the length of a line segment passing through the center whose ...A circle is the set of points in a plane that lie a fixed distance, called the radius, from any point, called the center. The diameter is the length of a line segment passing through the center whose endpoints are on the circle. In addition, a circle can be formed by the intersection of a cone and a plane that is perpendicular to the axis of the cone.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_372%3A_College_Algebra_for_Calculus/08%3A_Hooked_on_Conics/8.02%3A_CirclesRecall from Geometry that a circle can be determined by fixing a point (called the center) and a positive number (called the radius) as follows.
- https://math.libretexts.org/Courses/Coastline_College/Math_C170%3A_Precalculus_(Tran)/08%3A_Further_Applications_of_Trigonometry/8.05%3A_Polar_Coordinates_-_Graphspolar equation describes a relationship between rr and θ on a polar grid. It is easier to graph polar equations if we can test the equations for symmetry. There are three symmetry tests that indic...polar equation describes a relationship between rr and θ on a polar grid. It is easier to graph polar equations if we can test the equations for symmetry. There are three symmetry tests that indicate whether the graph of a polar equation will exhibit symmetry. If an equation fails a symmetry test, the graph may or may not exhibit symmetry.
- https://math.libretexts.org/Courses/Highline_College/MATHP_141%3A_Corequisite_Precalculus/05%3A_Exponential_and_Logarithmic_Functions/5.09%3A_Trigonometry_Preview_-_CirclesIf we were to expand the equation in the previous example and gather up like terms, instead of the easily recognizable \((x+2)^2 + (y-1)^2 = 4\), we'd be contending with \(x^2 + 4x + y^2 - 2y + 1 = 0....If we were to expand the equation in the previous example and gather up like terms, instead of the easily recognizable \((x+2)^2 + (y-1)^2 = 4\), we'd be contending with \(x^2 + 4x + y^2 - 2y + 1 = 0.\) If we're given such an equation, we can complete the square to rewrite the equation in standard form for a circle. The diameter of the circle is the distance between the given points, so we know that half of the distance is the radius.
- https://math.libretexts.org/Bookshelves/Algebra/Intermediate_Algebra_for_Science_Technology_Engineering_and_Mathematics_(Diaz)/13%3A_Introduction_to_Conics/13.02%3A_CirclesAs we discussed in the previous section, we see a circle is simply a cut from a right circular cone. Let’s discuss the properties of the circle and then graph it.
- https://math.libretexts.org/Bookshelves/Precalculus/Book%3A_Precalculus__An_Investigation_of_Functions_(Lippman_and_Rasmussen)/05%3A_Trigonometric_Functions_of_Angles/5.01%3A_CirclesIf we wanted to find an equation to represent a circle with a radius of r centered at a point ( h , k ), we notice that the distance between any point ( x , y ) on the circle and the center point ...If we wanted to find an equation to represent a circle with a radius of r centered at a point ( h , k ), we notice that the distance between any point ( x , y ) on the circle and the center point is always the same: r.
- https://math.libretexts.org/Bookshelves/Applied_Mathematics/Math_For_Liberal_Art_Students_2e_(Diaz)/06%3A_Geometry/6.02%3A_Perimeter_Circumference_and_AreaQuadrilaterals are a special type of polygon. As with triangles and other polygons, quadrilaterals have special properties and can be classified by characteristics of their angles and sides. Understan...Quadrilaterals are a special type of polygon. As with triangles and other polygons, quadrilaterals have special properties and can be classified by characteristics of their angles and sides. Understanding the properties of different quadrilaterals can help you in solving problems that involve this type of polygon.
