Ax 2 + Bxy + Cy 2 + Dx + Ey + F=0 General Equation of a Conic Section:

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Ax 2 + Bxy + Cy 2 + Dx + Ey + F=0 General Equation of a Conic Section:

Conic Sections ©Mathworld

Ellipses... where A & C have the SAME SIGN For example:

Ellipses... where A & C have the SAME SIGN and the same value you’ll have a circle For example: Ellipses...

circle center A circle is the set of all points in a plane equidistant from a fixed point called the center. Circle Center GEOMETRICAL DEFINITION OF A CIRCLE

radius The equation of a circle is derived from its radius. (h,k) (x,y)

distance formula the equation for the circle Use the distance formula to find an equation for x and y. This equation is also the equation for the circle. (h,k) (x,y)

THE DISTANCE FORMULA Next (h,k) (x,y)

(h,k) (x,y)

center (3,3) radius = 2

Ellipse An ellipse is the set of all points (x, y) in the plane such that the sum of the distances from (x, y) to two fixed points is some constant. The two fixed points are called the foci, which is the plural of focus.

Ellipse The standard form of the ellipse with a center at (h,k) is……

Ellipse –a is the horizontal distance from the center to each vertex. –Twice the distance from the center to each vertex is the length of the major axis. –b is the vertical distance from the center to each co-vertex. –Twice the distance from the center to each co-vertex is the length of the minor axis.

Ellipses... to convert equations from general to standard +1+4

–The center is at (1,-2). –The vertices are at (1,2) and (1,-6) –The length of the major axis is eight. –The co-vertices are at (3,-2) and (-1,-2). –The length of the minor axis is 4.

The center is at (1,-2). The vertices are at (1,2) and (1,-6) The length of the major axis is eight. The co-vertices are at (3,-2) and (-1,-2). The length of the minor axis is 4.