SOLUTION: Find the standard form of the equation of the ellipse with the given characteristics. Center: (6, 7); a = 3c; foci: (2, 7), (10, 7)

Question 1136850: Find the standard form of the equation of the ellipse with the given characteristics. Center: (6, 7); a = 3c; foci: (2, 7), (10, 7)
Found 2 solutions by greenestamps, MathLover1:
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

c is the distance from the center of the ellipse to each focus. The coordinates of the center and the two foci tell us c=4; that makes a, the semi-major axis, 3c = 12.

a, b, and c in an ellipse are related by c^2 = a^2-b^2; that gives us b, the semi-minor axis, equal to 8*sqrt(2).

The standard form of the equation of an ellipse with center (h,k), semi-major axis a, and semi-minor axis b is

You have all the numbers to fill in to write the equation.
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
Find the standard form of the equation of the ellipse with the given characteristics.
Center: (, );
;
foci: (, ), (, )

The equation of an ellipse is :
for a horizontally oriented ellipse and
for a vertically oriented ellipse.
(,) is the center and the distance from the center to the foci is given by

is the distance from the center to the vertices and is the distance from the center to the co-vertices.
The center of the ellipse is (, )=> and
is the distance between the center and the vertices, so
is the distance between the center and the foci, and foci is at (, ), (, )
distance from to is , and distance from to is
so
since , we have =>
now find

for a horizontally oriented ellipse

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