SOLUTION: Find an equation in standard form for the ellipse that satisfies the given conditions. Major axis endpoints ​(6​,6​) and ​(6​,-12​), minor axis length 4.

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find an equation in standard form for the ellipse that satisfies the given conditions. Major axis endpoints ​(6​,6​) and ​(6​,-12​), minor axis length 4.      Log On


   

Question 1134790: Find an equation in standard form for the ellipse that satisfies the given conditions.
Major axis endpoints ​(6​,6​) and ​(6​,-12​), minor axis length 4.
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

an equation in standard form for the ellipse is:
x%5E2%2Fa%5E2%2By%5E2%2Fb%5E2=1
given:
major axis is a
if endpoints ​(6​,6​) and ​(6​,-12%E2%80%8B%29%2C+the+distance+between+them+will+be+the+length+of+%7B%7B%7Ba
a=sqrt%28%286-6%29%5E2%2B%286-%28-12%29%29%5E2%29
a=sqrt%280%2B%286%2B12%29%5E2%29
a=sqrt%28%2818%29%5E2%29
a=18

minor axis length b=4
x%5E2%2F18%5E2%2By%5E2%2F4%5E2=1


Answer by ikleyn(52797) About Me  (Show Source):
You can put this solution on YOUR website!
.

            The solution by  @MathLover1  is   a b s o l u t e l y   w r o n g   and   t o t a l l y   i r r e l e v a n t.

            For your safety simply ignore it.

            I came to bring the correct solution - see below. 


From the given information, the center of the ellipse is at the point (6,-3).



The major axis length is 6+12 = 18 units.

Hence, the major semi-axis is 18/2 = 9 units long.

The major axis is vertical, parallel to y-axis.


The minor axis is parallel to x-axis; the minor semi-axis has the length of 2.



At this point, we just can write the standard equation of the ellipse


    %28x-6%29%5E2%2F2%5E2 + %28y%2B3%29%5E2%2F9%5E2 = 1.