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equations for ellipse. The standard equation of an ellipse is x2a2 y2b21. The focus points for the ellipse are at F 1 and F 2.
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One focus is located at 6 2 and its associated directrix is represented by the line x 11. C is the length from one foci to the center hence c 2. X a cos t.
Of these lets derive the equation for the ellipse shown in Fig5 a with the foci on the x-axis.
For an arbitrary point the distance to the focus is and to the other focus Hence the point is on the ellipse whenever. Multiply both sides of the equation by a2 to get x2y2a2 which is the standard equation for a circle with a radius of a. An ellipse can be defined as the locusof all points that satisfy the equations. Xy are the coordinates of any point on the ellipse a b are the radius on the x and y axes respectively See radii notes below tis the parameter which ranges from 0 to 2p radians.
