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The equation of an ellipse whose focus is $(- 1, 1)$ and whose directrix is $x - y + 3 = 0$ and eccentricity is $\frac{1}{2}$ is -

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Important Questions on Conic Sections

EASY

Mathematics>Coordinate Geometry>Conic Sections>Ellipse

The conic represented by

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

MEDIUM

Mathematics>Coordinate Geometry>Conic Sections>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

MEDIUM

Mathematics>Coordinate Geometry>Conic Sections>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

MEDIUM

Mathematics>Coordinate Geometry>Conic Sections>Ellipse

If the length of a rectangle is decreased by

5

metres and breadth increased by

3

metres, its area decreases by

9 m^{2}

. If its length is increased by

3 m

and breadth by

2 m

, its area increases by

67

m^{2}

. What is the length of the rectangle ?

EASY

Mathematics>Coordinate Geometry>Conic Sections>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

EASY

Mathematics>Coordinate Geometry>Conic Sections>Ellipse

If the interior angle of a regularpolygon is $108 °$ , then it is a-

1. Octagon

2. Hexagon

3. Pentagon

4. Tetragon

MEDIUM

Mathematics>Coordinate Geometry>Conic Sections>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:

EASY

Mathematics>Coordinate Geometry>Conic Sections>Ellipse

Read the given question and decide which of the following information is sufficient to answer the question.

What is the value of 0?

Information :

Question Image

(II) 0 < q < 90°

MEDIUM

Mathematics>Coordinate Geometry>Conic Sections>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:

MEDIUM

Mathematics>Coordinate Geometry>Conic Sections>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

MEDIUM

Mathematics>Coordinate Geometry>Conic Sections>Ellipse

The exterior angle of a regular polygon is

72 °

. What would be the sum of all its interior angles?

MEDIUM

Mathematics>Coordinate Geometry>Conic Sections>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)

MEDIUM

Mathematics>Coordinate Geometry>Conic Sections>Ellipse

$5 : 18$ is the ratio of the length and perimeter of a rectangle. What would be the ratio of its length and breadth?

EASY

Mathematics>Coordinate Geometry>Conic Sections>Ellipse

A hall is

15 m

long and

12 m

broad. The sum of the areas of the floor and the ceiling is?(in square meters).

MEDIUM

Mathematics>Coordinate Geometry>Conic Sections>Ellipse

∆ A B D

C

is the midpoint of

B D

. If

A B

= 10

cm, AD

= 12

cm and

A C

= 9

cm, then

B D = ?

EASY

Mathematics>Coordinate Geometry>Conic Sections>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

EASY

Mathematics>Coordinate Geometry>Conic Sections>Ellipse

In the given diagram, point R and Q are on PS. ÐPQT = x°, ÐRQT = (x – 50)° and ÐTUR = (x + 25°). find the value of ÐURS.

Question Image

EASY

Mathematics>Coordinate Geometry>Conic Sections>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

HARD

Mathematics>Coordinate Geometry>Conic Sections>Ellipse

If the distance between the foci of an ellipse is half the length of its latus rectum, then the eccentricity of the ellipse is:

MEDIUM

Mathematics>Coordinate Geometry>Conic Sections>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 equation of an ellipse whose focus is -1,1 and whose directrix is x - y + 3=0 and eccentricity is 12 is -

Important Questions on Conic Sections

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The equation of an ellipse whose focus is $(- 1, 1)$ and whose directrix is $x - y + 3 = 0$ and eccentricity is $\frac{1}{2}$ is -