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A conic is the curve obtained as the intersection of a plane, called the cutting plane, with the surface of a double cone (a cone with two nappes).It is usually assumed that the cone is a right circular cone for the purpose of easy description, but this is not required; any double cone with some circular cross-section will suffice.
In mathematics, the matrix representation of conic sections permits the tools of linear algebra to be used in the study of conic sections. It provides easy ways to calculate a conic section's axis , vertices , tangents and the pole and polar relationship between points and lines of the plane determined by the conic.
In Euclidean geometry, a circumconic is a conic section that passes through the three vertices of a triangle, [1] and an inconic is a conic section inscribed in the sides, possibly extended, of a triangle. [2] Suppose A, B, C are distinct non-collinear points, and let ABC denote the triangle whose vertices are A, B, C.
The equation for a conic section with apex at the origin and tangent to the y axis is + (+) = alternately = + (+) where R is the radius of curvature at x = 0. This formulation is used in geometric optics to specify oblate elliptical ( K > 0 ), spherical ( K = 0 ), prolate elliptical ( 0 > K > −1 ), parabolic ( K = −1 ), and hyperbolic ( K ...
In algebraic geometry, the conic sections in the projective plane form a linear system of dimension five, as one sees by counting the constants in the degree two equations. The condition to pass through a given point P imposes a single linear condition, so that conics C through P form a linear system of dimension 4.
requiring a conic to pass through a point imposes a linear condition on the coordinates: for a fixed (,), the equation + + + + + = is a linear equation in (,,,,,); by dimension counting , five constraints (that the curve passes through five points) are necessary to specify a conic, as each constraint cuts the dimension of possibilities by 1 ...
6 points on the sides of triangle and their common conic section. Carnot's theorem (named after Lazare Carnot) describes a relation between conic sections and triangles.. In a triangle with points , on the side , , on the side and , on the side those six points are located on a common conic section if and only if the following equation holds:
Media in category "Conic sections" This category contains only the following file. Drawing an ellipse via two tacks a loop and a pen 2.jpg 480 × 640; 24 KB