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## Ellipses

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**Ellipses**Topic 7.4**Definitions**• Ellipse: set of all points where the sum of the distances from the foci is constant • Major Axis: axis on which the foci lie; the longer axis of symmetry • Minor Axis: the shorter axis of symmetry**Two Standard Equations**• Horizontal Ellipse: • Foci: • Vertical Ellipse: • Foci:**Writing in Standard Form**• Complete the square for both the x-terms and y-terms and move the constant to the other side of the equation • Divide all terms by the constant**Example:**Group terms Complete the square Simplify each group Divide by constant**Graphing the ellipse**• Put equation in standard form • Graph the center (h, k) • Graph the foci (look at the equation to determine your direction) • Graph a units and –a units from the center to get the end points (horizontally if under x, vertically if under y) • Connect the end points!**Example:**1) Graph Center 2) Graph Foci 3) Graph Endpoints 4) Graph Ellipse**You Try!Write the following equation in standard form, then**graph it.