Problem :
Is the major axis of the following ellipse horizontal or vertical:
+ 
= 1?
a > b, and
6 > 4. Therefore,
a2 is the denominator of the
x2 term, so
the axis is horizontal.
Problem :
Find a, b, and c of the ellipse 
+ 
= 1.
a = 5,
b = 4, and
c = 
= 3.
Problem :
Find a, b, and c of the ellipse 9x2 +3y2 - 36x - 6y + 12 = 0.
By completing the square and factoring, you arrive at the standard equation
for an ellipse.
a = 3,
b = 
, and
c = 
.
Problem :
Find the vertices of the ellipse 2x2 +3y2 - 6 = 0.
a = , the major axis is horizontal, and the center of the ellipse
is
(0, 0). The vertices are at
(, 0) and
(- , 0).
Problem :
What is the eccentricity of the ellipse 81x2 + y2 - 324x - 6y + 252 = 0?
After completing the square and converting the equation to standard form, you
find
a = 9,
b = 1, and
c = 
. Therefore,
e = 
= 
.
Problem :
What is the center and radius of the circle x2 + y2 - 8x - 16y + 60 = 0?
Center:
(4, 8); Radius =
= 2
.
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