The Equation Of The Ellipse Whose Axes Are Along The Coordinate Axes, Vertices Are (0, ±10) And Eccentricity e = 4/5, Is

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Question

The equation of the ellipse whose axes are along the coordinate axes, vertices are (0, ±10) and eccentricity e = 4/5, is

easy

Solution

Correct option is

Let the equation of the required ellipse be

Since the vertices of the ellipse are on y-axis. So, the coordinates of the vertices are (0, ±b).

∴ b = 10

The eccentricity e is given by

Substituting the values of a² and b² in (i), we obtain

as the equation of the required ellipse.

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SIMILAR QUESTIONS

Q1

The equation represents an ellipse, if

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Q2

The curve with parametric equations

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Q3

The curve represented by

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Q4

Length of the major axis of the ellipse , is

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Q5

The length of the axes of the conic 9x² + 4y² – 6x + 4y + 1 = 0 are

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Q6

The eccentricity of the ellipse

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Q7

If the eccentricities of the two ellipse

are equal, then the value , is

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Q8

The curve represented by the equation

, is

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Q9

The equation of the ellipse whose axes are along the coordinate axes, vertices are (±5, 0) are foci at (±4, 0), is

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Q10

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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