Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 4 - Conic Section>4.2.1>Q 9

MEDIUM

JEE Main

IMPORTANT

Earn 100

Find the equation of the ellipse having ends of major axis $(0, \pm \sqrt{5})$ and ends of minor axis $(\pm 1, 0)$ .

Important Questions on Conic Section

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 4 - Conic Section>4.2.1>Q 10

If

a

be the length of semi-major axis,

b

the length of semi-minor axis and

c

the distance of one focus from the centre of an ellipse, then find the equation of the ellipse for which centre is

(0, 0),

foci is on

x

-axis,

b = 3

and

c = 4 .

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 4 - Conic Section>4.2.1>Q 11

The distance between the foci of an ellipse is

10

and its latus rectum is

15;

find its equation referred to its axes as axes of coordinates.

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 4 - Conic Section>4.2.1>Q 12

Find the equation of the ellipse in the standard form whose minor axis is equal to the distance between foci and whose latus-rectum is

10

EASY

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 4 - Conic Section>4.2.1>Q 13

The eccentricity of an ellipse is

\frac{1}{2}

and the distance between its foci is

4

units. If the major and minor axes of the ellipse are respectively along the

x

and

y

axes, find the equation of the ellipse.

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 4 - Conic Section>4.2.1>Q 14

Find the equation of the ellipse passing through

(6, 4),

foci on

y

-axis, centre at the origin and having eccentricity

\frac{3}{4}

.

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 4 - Conic Section>4.2.1>Q 15

Find the equation of the ellipse passing through

(4, 1)

with focus as

(\pm 3, 0)

.

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 4 - Conic Section>4.2.1>Q 16

Find the equation of the set of all points whose distances from

(0, 4)

are

\frac{2}{3}

of their distances from the line

y = 9

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 4 - Conic Section>4.2.1>Q 17

Find the equation to the ellipse whose foci are

(4, 0)

and

(- 4, 0)

and eccentricity is

\frac{1}{3}

.