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CONIC SECTIONS - ELLIPSES Example 5: Find the standard form of the equation of the ellipse having fo

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The document discusses the process of finding the standard form of the equation of an ellipse with given foci and a vertex. It emphasizes the importance of graphing to identify the orientation and center of the ellipse, which is determined to be at (-1, 2). The values for 'a' and 'b' are calculated based on the distances from the center to the foci and vertices, leading to the formulation of the standard equation for the ellipse.

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What is the standard form of the ellipse?

In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special type of ellipse in which the two focal points are the same.

What is the general form of the ellipse?

An ellipse is the locus of all those points in a plane such that the sum of their distances from two fixed points in the plane, is constant. The fixed points are known as the foci (singular focus), which are surrounded by the curve. The fixed line is directrix and the constant ratio is eccentricity of ellipse.

How do you find the standard form of the equation of an ellipse?

Equation of an Ellipse: The standard form of an equation of an ellipse is given by the equation ( x h ) 2 a 2 + ( y k ) 2 b 2 = 1 where is the center, is the distance from the center to the horizontal vertices and is the distance from the center to the vertical vertices.

What is the ellipse form?

ellipsoid, closed surface of which all plane cross sections are either ellipses or circles. An ellipsoid is symmetrical about three mutually perpendicular axes that intersect at the centre. If a, b, and c are the principal semiaxes, the general equation of such an ellipsoid is x2/a2 + y2/b2 + z2/c2 = 1.

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