SOLUTION: endpoints of major axis at (-11,5) and (7,5), endpoints of minor axis at (-2,9) and (-2,1)

Question 35840This question is from textbook Algebra 2
: endpoints of major axis at (-11,5) and (7,5), endpoints of minor axis at (-2,9) and (-2,1) This question is from textbook Algebra 2

Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
endpoints of major axis at (-11,5) and (7,5), endpoints of minor axis at (-2,9) and (-2,1)
PLEASE COPY PROBLEM PROPERLY..WHAT DO OU WANT?WHAT IS THE QUESTION?
I ASSUME IT IS TO FIND THE EQN.OF AN ELLIPSE!..OK..
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SEE THE FOLLOWING AND TRY BY YOUR SELF
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Can you help me write an equation for an ellipse with
a major axis with endpoints of (0,8), and (0,-8) with
foci of (0,5) and (0,-5)?
1 solutions
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Answer 16810 by venugopalramana(1120) on 2006-03-13
11:19:12 (Show Source):
Can you help me write an equation for an ellipse with
a major axis with endpoints of (0,8), and (0,-8) with
foci of (0,5) and (0,-5)?
THIS SHOWS THAT X AXIS IS THE MAJOR AXIS
STANDARD EQN.OF ELLIPSE IS
(X-H)^2/A^2 +(Y-K)^2/B^2=1
CENTRE IS (H,K)..AS PER THE PROBLEM H=K=0 AS CENTRE OF
ELLIPSE IS AT (0,0)..SINCE major axis with endpoints
ARE (0,8), and (0,-8)
WHERE MAJOR AXIS =2A=8+8=16...SO A=8..SINCE major axis
with endpoints ARE (0,8), and (0,-8)
FOCI ARE GIVEN BY
AE,0 AND -AE,0...SO AE =5...SO E=5/A=5/8
BUT E=SQRT{(A^2-B^2)/A^2}=5/8...SQUARING
25/64=(A^2-B^2)/A^2=1-B^2/A^2
B^2/64=1-25/64=49/64
B^2=49
B=7
HENCE EQN. OF ELLIPSE IS
X^2/64 + Y^2/49 = 1
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