SOLUTION: Find an equation of the ellipse that has center (1,4) , a minor axis of length 6 , and a vertex at (1,9). answer
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Question 1159590: Find an equation of the ellipse that has center (1,4) , a minor axis of length 6 , and a vertex at (1,9). answer
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
Determine whether the major axis is on the x - or y-axis.
If the given coordinates of the vertices and foci have the form (±,) and (±,) respectively, then the major axis is parallel to the x-axis. Use the standard form:
If the given coordinates of the vertices and foci have the form (,±) and (,±) respectively, then the major axis is parallel to the x-axis. Use the standard form:
given:
a vertex at (,)=> is the form (,±)
so, go with
if the center is at (,)=> and
if the length of minor axis is =>=>
(,)=>use to find
your equation is:
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
The length of the semi-major axis is the distance from the center to a vertex. The center is (1,4); one vertex is (1,9); the length of the semi-major axis is 5, and it is in the y direction.
Minor axis length 6 means length of semi-minor axis is 3. Since the major axis is in the y direction, the minor axis is in the x direction.
The general equation of an ellipse with center (h,k), semi-major axis a in the y direction and semi-minor axis b in the x direction is
Plug in the numbers we were given or have found:
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