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Circle Ellipse

Conic Sections. See video!. Circle Ellipse. Parabola Hyperbola. Circle. Standard Equation of a Circle:. P ( x, y ). (with radius of r and center at ( h,k ):. 2. 2. 2. (. –. ). + (. –. ). =. > 0. x. h. y. k. r. r. C ( h, k ).

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Circle Ellipse

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  1. Conic Sections See video! Circle Ellipse Parabola Hyperbola

  2. Circle Standard Equation of a Circle: P(x, y) (with radius of r and center at (h,k): 2 2 2 ( – ) + ( – ) = > 0 x h y k r r C(h, k) With center at (0,0), this simplifies to: x2 + y2 = r2

  3. Completing the Square To complete the square of the quadratic expression add the square of one-half the coefficient of x; that is, add The resulting expression can be factored as a perfect square:

  4. Reflective properties of parabola and ellipse: • Focus of Parabola • Reflective Properties of Ellipses

  5. Where do parabolas occur?

  6. Standard Equations of a Parabola with Vertex at (0, 0) 1.y = ax2 Vertex: (0, 0) Symmetric with respect to the y-axis. Vertex: (h, k) a > 0 (opens up) a < 0 (opens down) 2.x = ay2 Vertex: (0, 0) Symmetric with respect to the x-axis. Vertex: (h, k) a < 0 (opens left) a > 0 (opens right)

  7. Occurrences/uses of an ellipse?

  8. Standard Equations of an Ellipse with Center at (0, 0)

  9. Standard Equations for Translated Conics—II Ellipses

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