SOLUTION: Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Foci: (±5, 0); major axis of length 12

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Question 1151234: Find the standard form of the equation of the ellipse with the given characteristics and center at the origin.
Foci: (±5, 0); major axis of length 12
Found 2 solutions by pavan sai reddy, greenestamps:
Answer by pavan sai reddy(3) (Show Source):
You can put this solution on YOUR website!
Given that,

ae=5------------1 (where a is the semimajor axis
e is eccentricity )

and given 2a=12

=> a=6--------2

-> put 2 in 1 ,you will get

e=5/6
squaring on both sides

e^2=25/36 [we know that
e^2=1-b^2/a^2 where b=semi minoraxies]
=> 1-b^2/a^2=25/36

=> 1-b^2/36=25/36 (a=6 from 2)

=> 36-b^2=25
=> b^2=11--------------3

we know that the standard equation of ellipse looks like x^2/a^2+y^2/b^2=1
we know a^2=36(from 2) and b^2 =11(from 3)

now the equation becomes x^2/36+y^2/11=1

Answer by greenestamps(13200) (Show Source):
You can put this solution on YOUR website!

Foci (±5, 0) --> center at (0,0); major axis is horizontal; c=5
Major axis length 12 --> semimajor axis = 6 = a

where

So

Equation: