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Question 76855: write in standard form
an ellipse with major axis 6 units long and parallel to the x-axis minor axis 4 units long, and center at (8,6)
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website!
Learn the two ellipse rules:
1. An ellipse with major axis parallel to the x-axis has equation
Where (h,k) is the center, "a" is one-half the major axis and
and "b" is one-half the minor axis. The foci are the points
(h+c,k) and (h-c,k) where  . You can
always tell which is aČ and which is bČ because aČ is ALWAYS
larger than bČ.
2. An ellipse with major axis parallel to the y-axis has equation
Where (h,k) is the center, "a" is one-half the major axis and
and "b" is one-half the minor axis. The foci are the points
(h,k+c) and (h,k-c) where . You can
always tell which is aČ and which is bČ because aČ is ALWAYS
larger than bČ.
Your problem is on the first type
an ellipse with major axis 6 units long and parallel to the
x-axis; minor axis 4 units long; and center at (8,6)
a = 1/2 the major axis = (1/2)(6) = 3
b = 1/2 the minor axis = (1/2)(4) = 2
(h,k) = (8,6)
Substitute in
and get
or
The graph is
Edwin
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