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Question

If the equation (5x1)2+(5y2)2=(λ22λ+1)(3x+4y1)2 represents an ellipse, then

A
λ(0,2){1}
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B
λ(0,2)
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C
λ(0,1)
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D
λ(0,1]
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Solution

The correct option is A λ(0,2){1}
Given equation of ellipse is
(x15)2+(y25)2=(λ1)2[3x+4y132+42]2
(x15)2+(y25)2=|(λ1)||3x+4y1|32+42
It represents an ellipse with focus at (15,25) and directrix as 3x+4y1, then eccentricity lies in (0,1)
0<|λ1|<11<λ1<1λ(0,2){1}

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