Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 63

EASY

JEE Main

IMPORTANT

Earn 100

If the sum of the tangents of the base angles of a triangle described on a given base be constant, show that the locus of its vertex is a parabola.

Important Questions on Conic Section

EASY

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 64

Prove that the locus of the centres of equilateral triangles inscribed in the parabola

y^{2} = 4 a x

is

9 y^{2} = 4 a (x - 8 a) .

EASY

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 71

If the tangents at the points

P

and

Q

on the parabola

y^{2} = 4 a x

meet at

R

and

S

is its focus, prove that

S R^{2} = S P . S Q .

EASY

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 78

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 7 - Conic Section>7.1>Q 79

Find the equation to the ellipse (referred to its axes as the axes of

x

and

y

respectively) which passes through the point

(- 3, 1)

and has eccentricity

\sqrt{\frac{2}{5}}

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 80

Find the latus rectum, eccentricity, coordinates of the foci and the length of axes of the ellipse

4 x^{2} + 9 y^{2} - 8 x - 36 y + 4 = 0

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 81

Find the eccentric angles of the point on the ellipse

x^{2} + 3 y^{2} = 6

at a distance

2

unit from its centre.

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 82

If the angle between the lines joining the foci of any ellipse to an extremity of the minor axis is

90 °,

find the eccentricity. Also find the equation of the ellipse if the major axis is

2 \sqrt{2}

.

EASY

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 83

Find the condition that the line

x \cos α + y \sin α = p

may be a tangent to the ellipse

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

Also find the point of contact.