Question 61314This question is from textbook
: Find the equation of the ellipse that has the four points as endpoints of the major and minor axes. (3,0), (-3,0), (0,5), (-5,0).
I tried to use the x^2/a^2 + y^2/b^2 = 1 but I got a lil confused as to which numbers to use for x,a,y,b
This question is from textbook
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! Find the equation of the ellipse that has the four points as endpoints of the major and minor axes. (3,0), (-3,0), (0,5), (-5,0).
I tried to use the x^2/a^2 + y^2/b^2 = 1
OK...BUT MORE GENERAL EQN. IS
(X-H)^2/A^2 + (Y-K)^2/B^2=1.....CENTRE IS (H,K)
WE FIND (3,0) AND (-3,0) ARE 2 ENDS OF ONE AXIS ..ITS LENGTH IS 6
...OBVIOUSLY IT IS THE X AXIS
CHECK YOUR OTHER END POINTS DID YOU TYPE PROPERLY?IS IT (-5,0)?OR (0,-5)
ASSUMING IT TO BE (0,-5) OBVIOUSLY THE OTHER AXIS IS Y AXIS.ITS LENGTH IS 10
THEN VERTEX IS (0,0)...THAT IS H=0 AND K=0 AS YOU HAVE PUT THE EQN.
NOW COMING TO YOUR OTHER QUESTION HERE AXIS ALONG X AXIS IS SHORTER
= 6 = 2A ..OR....A =3...SO WE CALL IT MINOR AXIS
AXIS ALONG Y AXIS IS LONGER = 10 = 2B..B=5...IT IS MAJOR AXIS.
SO EQN. IS
X^2/9 + Y^2/25 =1
YOU CAN CHECK THE POINTS BY SUBSTITUTION .
but I got a lil confused as to which numbers to use for x,a,y,b
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