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Eccentricity of Ellipse

The eccentric...

Question

The eccentricity of the ellipse $3 x^{2} + 2 y^{2} = 6$ is $\sqrt{3}$ .

A

False

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B

True

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Solution

The correct option is A False

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Q. Assertion :Equation of an ellipse is of the form

3 x^{2} + 2 y^{2} = 6

, then its eccentricity '

e

\frac{1}{\sqrt{2}}

. Reason: The eccentricity '

e

' of the ellipse is given by,

e = \sqrt{1 - \frac{a^{2}}{b^{2}}}

For the given ellipse, find the length of major and minor axes, coordinates of foci and vertices and the eccentricity.

3 x^{2} + 2 y^{2} = 6

Q. The area bounded by the ellipse

3 x^{2} + 2 y^{2} = 6

with the co-ordinate axes in sq. units is

Q. An ellipse intersects the hyperbola

2 x^{2} - 2 y^{2} = 1

orthogonally. The eccentricity of the ellipse is reciprocal of that of the hyperbola. If the axes of the ellipse are along the coordinates axes, then

Q. An ellipse intersects the hyperbola

2 x^{2} - 2 y^{2} = 1

orthogonally. The eccentricity of the ellipse is the reciprocal of that of hyperbola. If the axis of the ellipse are along the coordinate axis, then

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