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In implicit form, the equation is: A x^2 + B x y + C y^2 + D x + E y + F = 0 (although there are varients, e.g. writing 2B instead of B or putting F on the right). For some choices of the coefficients A, B, C, D, E, and F the form is degenerate, in which case the equation may have no solution (e.g. A, B, C, D, E are all zero, F is not) or they may represent one or two lines.
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Which Conic sections describes a closed curve?
Circles, parabolas, ellipses, and hyperbolas are all conic sections. Out of these conic sections, the circle and ellipse are the ones which define a closed curve.
Why are conic section called conic sections?
Circles, ellipses, parabolas, and hyperbolas are called conic sections because they can be obtained as a intersection of a plane with a double- napped circular cone. If the plane passes through vertex of the double-napped cone, then the intersection is a point, a pair of straight lines or a single line. These are called degenerate conic sections. Because they are sections of a cone or a cone shaped object.
What conic sections represent a closed curve?
Ellipse circle
Where can you find conic sections in the world around you?
You can find them in mountains, in balls, and in tables.
Why are conic sections called conic?
They are the shapes of the slices when you slice a cone. For example, when you slice it parallel to the base and look at the shape of the slice, you see the conic section known as a "circle". The others are the "ellipse", the "parabola", and the "hyperbola". Which one you get depends only on how you tilt the knife when you slice the cone.
