Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 4 - Conic Section>4.1.1>Q 28

MEDIUM

JEE Main

IMPORTANT

Earn 100

The focus of a parabolic mirror as shown in the figure alongside is at a distance of $6 cm$ from its vertex. If the mirror is $20 cm$ deep, find the distance $LM$ .

Important Questions on Conic Section

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 4 - Conic Section>4.1.1>Q 29

A water jet from a fountain reaches its maximum height of

4

metres at a distance of

0.5

metres from the vertical passing through the point

O

of the water outlet. Find the height of the jet above the horizontal

O X

at a distance

0.75

metres from the point

O

.

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 4 - Conic Section>4.1.1>Q 30

The tower of a bridge, hung in the form of a parabola have their tops

30

meters above the roadway and are

200

meters apart. If the cable is

5

meters above the road way at the centre of the bridge, find the length of the vertical supporting cable from the centre.

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 4 - Conic Section>4.2.1>Q 1

Find the equation of the ellipse whose focus is

(- 1, 1)

directrix is

x - y + 3 = 0

and eccentricity is

\frac{1}{2}

.

EASY

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 4 - Conic Section>4.2.1>Q 1

Find the equation to the ellipse whose
one focus is

(6, 7),

directrix is

x + y + 2 = 0

and eccentricity is

\frac{1}{\sqrt{3}}

.

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 4 - Conic Section>4.2.1>Q 2

Find the equation to the ellipse whose one focus is

(2, 1),

the directrix is

2 x - y + 3 = 0

and the eccentricity is

\frac{1}{\sqrt{2}}

.

EASY

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 4 - Conic Section>4.2.1>Q 3

Find the equation of an ellipse with center at the origin, the length of the major axis

12

and one focus at

(4, 0)

.

HARD

JEE Main

IMPORTANT

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

Find the equation of the ellipse whose centre is at

(- 2, 3)

and whose semi-axes are

3

and

2

when major axis is parallel to

y -

axis.

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 4 - Conic Section>4.2.1>Q 5

Find the equation of an ellipse whose vertices are

(0, \pm 10)

and eccentricity

e = \frac{4}{5}