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Question 821906: find the foci of the conic section represented by the following equation 4x^2+25y^2=100
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! Given
(1) 4x^2 + 25y^2 = 100
Divide through by 100 to get
(2) (4/100)x^2 + (25/100)y^2 = 1 or
(3) (x^2)/25 + (y^2)/4 = 1 or
(4) (x/5)^2 + (y/2)^2 = 1 which is the standard form of the ellipse
(5) (x/a)^2 + (y/b)^2 = 1 where
(6) a = 5 and
(7) b = 2
The distance from the center (0,0) in x,y coordinates to either focal point is given by
(8) f = sqrt(a^2 - b^2) or
(9) f = sqrt(25-4) or
(10) f = sqrt(21)
Answer: The foci are at (x,y) = (+sqrt(21),0) and (-sqrt(21),0) or
approximately (4.58,0) and (-4.58,0).
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