The conic equation \ \

1) To identify the conic section \ \

General form of a conic equation inthe form \ \

Both variables are squared and have the same sign, but they aren\\'t multiplied by the same number, so this is an ellipse. \ \

is ellipse. \ \

2) To find the ellipse in standard form. \ \

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To change the expressions (x ²- 2x) and (y ² - 4y) into a perfect square trinomial, \ \

add (half the x coefficient)² and add (half the y coefficient)² to each side of the equation. \ \

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The standard form for an ellipse is in a form = 1, So divide both sides of equation by 4 to set it equal to 1. \ \

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Compare it to standard form of ellipse

a ² > b ² \ \

If the larger denominator is under the "x " term, then the ellipse is horizontal. \ \

3) Center (h, k ) = (1, 2) \ \

a  = length of semi-major axis = 2 \ \

b  = length of semi-minor axis = 1 \ \

Vertices: (h + a, k ), (h - a, k ) \ \

= (1+2, 2) ,(1-2, 2) \ \

Vertices are (3,2),(-1, 2) \ \

c  is the distance from the center to each focus. \ \

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Foci: (h + c, k ), (h - c, k ) \ \

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Foci (-0.73, 2), (2.73,2).

Ellipses do not have asymptotes. \ \

By definition, an asymptote is a line that a graph approaches, but never intersects. It is a limit for the graph. Ellipses do not have such limits. \ \

(h ,k ) = (1,2) ,a  = 2 and b  = 1

The points for this ellipse are ,

Right most point (h +a , k )

Left most point (h - a , k )

Top most point (h , k + b )

Bottom most point (h , k - b )

Right most point (3, 2)

Left most point (-1, 2)

Top most point (1, 3)

Bottom most point (1, 1)

Graph

1. draw the coordinate plane.

2. Plot the center at (0, 0).

3.Plot 4 points away from the center in the up, down, left and right direction.

4.Sketch the ellipse.

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