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If vertices of an ellipse are (–4, 1), (6, 1) and x – 2y = 2 is a focal chord then the equation of the ellipse

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$\frac{(x - 1)^{2}}{25} + \frac{(y - 1)^{2}}{16} = 1$

$\frac{(x - 1)^{2}}{25} + \frac{(y - 1)^{2}}{9} = 1$

$\frac{(x - 1)^{2}}{16} + \frac{(y - 1)^{2}}{25} = 1$

$\frac{(x - 1)^{2}}{9} + \frac{(y - 1)^{2}}{25} = 1$

answer is B.

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Detailed Solution

$C =(1,1), a = 5 \Rightarrow S =(1+ ae,1) = (1 + 5 e, 1) lieson x -2 y =2 \Rightarrow 1 + 5 e - 2 - 2 = 0 \Rightarrow e = \frac{3}{5} a n d b^{2} = 16$

Ellipse is $\frac{(x - 1)^{2}}{25} + \frac{(y - 1)^{2}}{16} = 1$

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