Ellipse

A locus of the point which is such that its distance from a fixed point and its distance from a fixed line bears a constant ratio and this ratio is usually less than 1. The fixed point is called the focus and the fixed line is called the directrix.

The equation of the parabola with focus at P(x1, y1) and directrix ax + by + c = 0 is √[(x - x1)2 + (y - y1)2] = e (ax1 + by1 + c)/[√(a2 + b2)]

Property\Equationx2/a2 + y2/b2 = 1 (a>b)y2/a2 + x2/b2 = 1 (a>b)
Major Axisy = 0x = 0
Minor Axisx = 0y = 0
Foci(±ae,0)(0,±ae)
Directricesx = ±a/ey = ±a/e
Vertex(±a,0)(0,±a)
Eccentricitye2 = 1 - b2/a2e2 = 1 - b2/a2



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