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9.3. Ellipse. Def: An ellipse is the collection of all points in the plane the sum of whose distances form two fixed points, called the foci (two), is a constant. . Def: Major axis : the line containing the foci
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9.3 Ellipse
Def: An ellipse is the collection of all points in the plane the sum of whose distances form two fixed points, called the foci (two), is a constant.
Def: Major axis: the line containing the foci Minor axis: the line through the center and perpendicular to the major axis Vertices: the points of intersection of the ellipse and the major axis
Equations: Center (0,0), MA: x – axis, foci at (c,0) and (-c,0). Where a > b > 0 and b2 = a 2 – c2 V(-a,0) and (a,0)
Equations: Center (0,0), MA: y – axis, foci at (0,c) and (0,-c). Where a > b > 0 and b2 = a 2 – c2 V(0,-a) and (0,a) If the bigger number is under y then it is up and down if the bigger number is under x then it is left and right.
When we shift an ellipse is just like when we moved circles or parabolas. The center becomes (h,k) so we subtract h from the x and k from the y. Be sure to also change your foci and vertices.
