Conic Sections: Overview of Ellipse ( Click Ellipse )
Definition: A elipse is a set of points whose sum of distances from two points (foci) is contant. *
Equation: x2 /a2 + y2 /b2 = 1 Center= (0,0) (x-h)2/a2 + (y-k)2/b2 = 1 Center = (h,k)
Important Concepts for Elipses: Center,
Foci, Axis,
Intercept(s)
Eccentricity (e=c/a & 0<e<1) Latus Rectum: LR = 2b2/a Foci Formula: a2 – c2 = b2
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Determine an equation for a Elipse with Center at (0,0): Major Axis of 6
and Minor Axis of 4.
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x2 /a2 + y2
/b2 = 1 |
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x2
/32 + y2 /22 = 1 |
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4x2 + 9y2 = 36 |
Determine an equation for a Circle with Center at (+2,+2) and Eccentricity of 1/2:
a2 – c2
= b2 22 + 12
= b2 4 + 1 = b2 b2 = 5 b = Ö5
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(x-h)2/a2 +
(y-k)2/b2 = 1 |
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(x-2)2/22 +
(y-2)2/Ö52 = 1 |
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x2 –4x +4 + y2
–4y +4 = 20 |
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x2 –4x + y2 –4y = 12 |
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