Conic Sections

When a double–napped right circular cone is cut into sections by a plane, the curves so formed are known as the conic sections or conics. A circle is the set of all the points in a plane that are equidistant from a fixed point in the plane. A parabola is the locus of all the points in a plane that are equidistant from a fixed line and a fixed point in the same plane. The fixed point is not on the fixed line. Parabola is symmetric with respect to the axis of the parabola. If the equation has a y2 term, then the axis of symmetry is along the x–axis and if the equation has x2 term, then the axis of symmetry is along the y–axis. A line segment which is perpendicular to the axis of the parabola, passes through the focus, and whose end points lie on the parabola is called the ‘latus rectum’ of the parabola. An ellipse is a set of all points in a plane, such that the sum of their distances from two fixed points in the plane is a constant. The eccentricity of an ellipse is the ratio of the distances from the centre of the ellipse to one of the foci and to one of the vertices. It is denoted by e. Ellipse is symmetric with respect to both the coordinate axes. The eccentricity of a hyperbola is the ratio of the distances from the centre of the hyperbola to one of the foci and to one of the vertices. Hyperbola is symmetric with respect to both the axes. A hyperbola in which a = b is called an equilateral hyperbola. Key Words: Latus Rectum of a hyperbola

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