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The sum of the focal distances of any point on an ellipse is equal to the length of the

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Important Questions on Ellipse

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Mathematics>Coordinate Geometry>Ellipse>Basics of Ellipse

An ellipse, with foci at

(0,2)

and

(0, - 2)

and minor axis of length

4

, passes through which of the following points?

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Mathematics>Coordinate Geometry>Ellipse>Basics of Ellipse

A focus of an ellipse is at the origin. The directrix is the line

x = 4

and the eccentricity is

1 / 2 .

Then the length of the semi-major axis is

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Mathematics>Coordinate Geometry>Ellipse>Basics of Ellipse

In an ellipse, with centre at the origin, if the difference of the lengths of major axis and minor axis is 10 and one of the foci is at

(0,5 \sqrt{3}),

then the length of its latus rectum is:

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Mathematics>Coordinate Geometry>Ellipse>Basics of Ellipse

The eccentricity of the ellipse

9 x^{2} + 25 y^{2} = 225

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Mathematics>Coordinate Geometry>Ellipse>Basics of Ellipse

Consider an ellipse, whose center is at the origin and its major axis is along the

x

-axis. If its eccentricity is

\frac{3}{5}

and the distance between its foci is

6

, then the area (in sq. units) of the quadrilateral inscribed in the ellipse, with the vertices as the vertices of the ellipse, is:

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Mathematics>Coordinate Geometry>Ellipse>Basics of Ellipse

If the distance between the foci of an ellipse is

6

and the distance between its directrix is

12,

then the length of its latus rectum is

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Mathematics>Coordinate Geometry>Ellipse>Basics of Ellipse

Let

O (0,0)

and

A (0,1)

be two fixed points. Then, the locus of a point

P

such that the perimeter of

Δ A O P

4

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Mathematics>Coordinate Geometry>Ellipse>Basics of Ellipse

S

and

T

are the foci of an ellipse and

B

is the end point of the minor axis. If

S T B

is equilateral triangle, the eccentricity of the ellipse is

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Mathematics>Coordinate Geometry>Ellipse>Basics of Ellipse

In an ellipse, its foci and the ends of its major axis are equally spaced. If the length of its semi-minor axis is

2 \sqrt{2},

then the length of its semi-major axis is

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Mathematics>Coordinate Geometry>Ellipse>Basics of Ellipse

Two sets

A

and

B

are as under:

A = \{(a, b) \in R \times R : |a - 5| < 1 and |b - 5| < 1\};

B = \{(a, b) \in R \times R : 4 {(a - 6)}^{2} + 9 {(b - 5)}^{2} \leq 36\} .

Then :

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Mathematics>Coordinate Geometry>Ellipse>Basics of Ellipse

The conic represented by

x = 2 (\cos t + \sin t), y = 5 (\cos t - \sin t)

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Mathematics>Coordinate Geometry>Ellipse>Basics of Ellipse

The equation of the circle passing through the foci of the ellipse

\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1

, and having centre at

(0, 3)

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Mathematics>Coordinate Geometry>Ellipse>Basics of Ellipse

If the length of the major axis of the ellipse

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

is three times the length of minor axis, its eccentricity is

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Mathematics>Coordinate Geometry>Ellipse>Basics of Ellipse

If the line

x - 2 y = 12

is a tangent to the ellipse

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

at the point

(3, - \frac{9}{2})

, then the length of the latus rectum of the ellipse is

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Mathematics>Coordinate Geometry>Ellipse>Basics of Ellipse

O T

is the semi-minor axis of an ellipse,

A

and

B

are its foci and

∠ A T B

is a right angle, then the eccentricity of that ellipse is

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Mathematics>Coordinate Geometry>Ellipse>Basics of Ellipse

A focus of an ellipse is at the origin. The directrix is the line

x = 4

and the eccentricity is

\frac{1}{2}

. The length of the semi-major axis is

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Mathematics>Coordinate Geometry>Ellipse>Basics of Ellipse

If a bar of given length moves with its extremities on two fixed straight lines at right angles, then the locus of any point on bar marked on the bar describes a/an

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Mathematics>Coordinate Geometry>Ellipse>Basics of Ellipse

If a point

P (x, y)

moves along the ellipse

\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1

and if

C

is the centre of the ellipse, then the sum of maximum and minimum values of

C P

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Mathematics>Coordinate Geometry>Ellipse>Basics of Ellipse

If the length of the latus rectum of an ellipse is

4

units and the distance between a focus and its nearest vertex on the major axis is

\frac{3}{2}

units, then its eccentricity is

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Mathematics>Coordinate Geometry>Ellipse>Basics of Ellipse

Let

S

and

S^{'}

be the foci of an ellipse and

B

be any one of the extremities of its minor axis. If

Δ S^{'} B S

is a right angled triangle with right angle at

B

and area

(Δ S^{'} B S) = 8 sq . units

, then the length of a latus rectum of the ellipse is :

The sum of the focal distances of any point on an ellipse is equal to the length of the

Important Questions on Ellipse

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