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Quiz review

8.4 ELLIPSES. Definition / featuresStandard form / features graphDeriving formulaFinding equation given featuresRewriting in standard form. Definition of ellipse. An ellipse is the set of points in a plane such that the sum of the distances from two fixed points (called foci) is constantSee

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Quiz review

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    1. Quiz review Circle equation: (x – h)2 + ( y – k)2 = r2 Recall relevant vocab: diameter, tangent For parabolas, either: y = a(x – h)2 + k OR: x = a(y – k)2 + h For parabolas, a = 1/4p, where p is the distance from the VERTEX to the focus and to the directrix FOR BOTH TYPES OF CONICS: - Given equation, find the features - Given some features, find the equation - Rewrite an equation in standard form (use completing the square) ALSO - know the distance and midpoint formula, review slope formula - Be able to show that segments are congruent, parallel, or perpendicular, or that one segment bisects another!

    2. 8.4 ELLIPSES Definition / features Standard form / features + graph Deriving formula Finding equation given features Rewriting in standard form

    3. Definition of ellipse An ellipse is the set of points in a plane such that the sum of the distances from two fixed points (called foci) is constant See graph on board Other features of ellipse: - center - major axis + endpoints - minor axis + endpoints

    4. Standard form of ellipse The standard form of an ellipse is: (x – h)2 + (y – k)2 = 1 a2 b2 Where (h,k) are the coords of the center a is ˝ the length of the major axis b is ˝ the length of the minor axis NOTE that a and b can switch places depending on the orientation of the ellipse! That is, if the ellipse is horizontally oriented (see board) then “a2” will be underneath the x-term… if the ellipse is vertically oriented, a2 will be underneath the y-term

    5. a, b, c The other feature of the ellipse, the foci, can be found using a and b We call c the distance from the center to a focus The relationship between a,b and c is: c2 = a2 – b2 So if we know a and b we can find the coordinates of the foci

    6. Example 4-3a

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