1CConics

= 1C Circles and Ellipses =


 * In this section we use a coordinate geometry approach to studying three types of relation.
 * We will look at
 * circles
 * ellipses
 * hyperbolas.


 * Circles **


 * The basic equation for a circle, with radius r, centered at the origin is:
 * x 2 + y 2 = r 2


 * The general equation for a circle, with radius r, centered at (h, k) is:
 * (x – h) 2 + (y – k) 2 = r 2


 * The parametric equations for a circle, with radius r, centered at (h, k) are:
 * x = r cos(t) + h
 * y = r sin(t) + k


 * Elllipses **


 * The basic equation for an ellipse, centered at the origin with x-radius = a and y-radius = b is:

math . \qquad \qquad \dfrac {x^2}{a^2} + \dfrac {y^2}{b^2} = 1 math


 * The general equation for an ellipse, centered at (h, k) with x-radius = a and y-radius = b is:

math . \qquad \qquad \dfrac {(x-h)^2}{a^2} + \dfrac {(y-k)^2}{b^2} = 1 math


 * The parametric equations for an ellipse centered at (h, k) are:
 * x = a cos(t) + h
 * y = b sin(t) + k

= Hyperbolas with Oblique Asymptotes (1D) =


 * The basic equation for a hyperbola with oblique asymptotes, centered at the origin is:

math . \qquad \qquad \dfrac {x^2}{a^2} - \dfrac {y^2}{b^2} = 1 math


 * This hyperbola has asymptotes with equations:

math . \qquad\qquad y = \pm \dfrac {b}{a} x math


 * The general equation for a hyperbola with oblique asymptotes, centered at (h, k) is:

math . \qquad \qquad \dfrac {(x-h)^2}{a^2} - \dfrac {(y-k)^2}{b^2} = 1 math


 * This hyperbola has asymptotes with equations:

math . \qquad \qquad y = \pm \dfrac {b}{a} (x - h) + k math


 * The parametric equations for a hyperbola centered at (h, k) are:
 * x = a sec(t) + h
 * y = b tan(t) + k

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