The Vertices Of The Ellipse

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Question

The vertices of the ellipse

None of these

easy

Solution

Correct option is

The equation of the ellipse can be written as

Shifting the origin at (1, 0), keeping the axes parallel to the coordinate axes, we have

The equation of the ellipse with reference to new origin is

The coordinates of vertices with reference to new origin are

.

Substituting these in (i), we obtain (1, ±3) as the coordinates of the vertices of the given conic.

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SIMILAR QUESTIONS

Q1

If the eccentricities of the two ellipse

are equal, then the value , is

easy View solution

Q2

The curve represented by the equation

, is

easy View solution

Q3

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

medium View solution

Q4

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

easy View solution

Q5

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

easy View solution

Q6

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

easy View solution

Q7

The equation of the circle drawn with the two foci of as the end-points of a diameter, is

easy View solution

Q8

The foci of the conic 25x² +16y² – 150x = 175 are

medium View solution

Q9

The foci of the ellipse are

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Q10

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

medium View solution