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Find the equation of the ellipse whose a...

Find the equation of the ellipse whose axes are of length 6 and `2sqrt(6)` and their equations are `x-3y+3=0` and `3x+y-1=0` , respectively.

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Length of major axiz is 6 which is along the line x-3y+3=0 and lengthof axis is `2sqrt(6)` which is along the line 3x+y-1=0
Thus, equation of ellipse is `(((3x+y-1)/(sqrt(9+1)))/(3))^(2)+(((x-3y+3)/(sqrt(1+9)))/(sqrt(6)))^(2)=1`
or `((3x+y-1))/(90)+((x-4y+3)^(2))/(60)=1`
`rArr2(3x+y-1)^(2)+3(x-3y+3)^(2)=180`
`rArr 21x^(2)-6xy+29y^(2)+6y-58y-151=0`
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