First slide

Ellipse

Question

$If (1,1) and (6, 1) are the vertices of an ellipse and one of whose foci lies on x - 2y = 2 then the eccentricity of ellipse is$

Moderate

A

$\frac{3}{5}$
B

$\frac{4}{5}$
C

$\frac{2}{5}$
D

$\frac{1}{5}$

Solution

$\begin{array}{l} Vertices are (- 4, 1) and (6, 1) . \\ ∴ 2 a = 10 \end{array}$
$Centre is (1, 1). Focus is at distance 'ae' from the centre.$
$∴ Focus (1 + 5 e, 1), which lies on x - 2 y = 2$
$\begin{array}{ll} ∴ 1 + 5 e - 2 = 2 \\ ∴ e = 3 / 5 \end{array}$

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