The Equation Of The Ellipse, With Axes Parallel To The Coordinate Axes, Whose Eccentricity Is 1/3 And Foci Are At (2, –2) And (2, 4) Is

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Question

The equation of the ellipse, with axes parallel to the coordinate axes, whose eccentricity is 1/3 and foci are at (2, –2) and (2, 4) is

None of these

medium

Solution

Correct option is

The centre of the ellipse is at the mid-point of its foci. So, coordinates of centre are (2, 1).

Clearly, two foci lie on the line x = 2. So, major axis is parallel to y-axis.

The distance between two foci is 6.

.

Now,

Hence, the equation of the ellipse is

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SIMILAR QUESTIONS

Q1

The curve represented by the equation

, is

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Q2

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Q3

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Q4

If the latusrectum of an ellipse is equal to one half of its minor axis, then the eccentricity is equal to

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Q5

The eccentricity of the ellipse, if the distance between the foci is equal to the length of the latusrectum, is

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Q8

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Q9

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Q10

For the ellipse

,

lengths of major and minor axes are respectively.

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