Circle Ellipse Parabola Hyperbola Conic Sections See video!

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Circle Ellipse Parabola Hyperbola Conic Sections See video!

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

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:

Reflective properties of parabola and ellipse: 1.Focus of ParabolaFocus of Parabola 2.Reflective Properties of EllipsesReflective Properties of Ellipses

Where do parabolas occur?

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

Occurrences/uses of an ellipse?

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

Ellipses Standard Equations for Translated Conics—II