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Find the foci of the ellipse 25(x+1)^2+9...

Find the foci of the ellipse `25(x+1)^2+9(y+2)^2=225.`

Text Solution

Verified by Experts

The correct Answer is:
`(-1,2)(-1,-6)`
The given equation can be wirtten as `((x+1)^(2))/(9)+((y+2)^(2))/(25)=1`
which represents an ellipse whose center is `(-1,-2`) and semi-major and the minor are 5 and 3, respectively.
The eccentricity of the ellipse is given by
`9=251-e^(2)or e=(4)/(5)`
Shifting the origin at (-1,-2), the given reduces to
`(x^(2))?(9)+(y^(2))/(25)=1" "(1)`
where `x=X-1,y=Y-2" "(2)`
The coordinates of the foci (1) are `(X=0,Y=+-be)`, where `b=5, e=4//5, i.e., the foci of (1) (X=0,Y+-4)`.
Therefore, the cooridnates of the foci of the given ellipse are (-1,-2) and (-6,-6)
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