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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