Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 4 - Conic Section>4.1.1>Q 22

MEDIUM

JEE Main

IMPORTANT

Earn 100

Find the focus and directrix of the parabola $3 x^{2} + 12 x + 8 y = 0$ .

Important Questions on Conic Section

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 4 - Conic Section>4.1.1>Q 23

Find the equation of the parabola with focus

(5, 0)

and directrix

x = - 5 .

Also, find the length of the latus rectum.

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 4 - Conic Section>4.1.1>Q 24

Find the equation of the circle described on the line segment joining the foci of the parabolas

x^{2} = 4 a y

and

y^{2} = 4 a (x - a)

as diameter.

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 4 - Conic Section>4.1.1>Q 25

An equilateral triangle is inscribed in the parabola

y^{2} = 4 a x

whose vertex is at the vertex of the parabola .find the length of the side of the triangle

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 4 - Conic Section>4.1.1>Q 26

Find the area of the triangle formed by lines joining the vertex of the parabola

x^{2} = 12 y

to the ends of its latus rectum.

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 4 - Conic Section>4.1.1>Q 27

P Q

is a double ordinate of a parabola

y^{2} = 4 a x

. Find the locus of its points of trisection.

MEDIUM

JEE Main

IMPORTANT

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

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 $LM$ .

Question Image

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.