Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 76

EASY

JEE Main

IMPORTANT

Earn 100

If a circle intersects the parabola $y^{2} = 4 a x$ in the points $A, B, C, D$ whose parameters with reference to the parabola are $t_{1}, t_{2}, t_{3}, t_{4},$ then show that $t_{1} + t_{2} + t_{3} + t_{4} = 0$

Important Questions on Conic Section

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - 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 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.

EASY

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 84

The distance of a point on the ellipse

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

from the centre is

2

. Find the eccentric angle of the point in the first quadrant. Also find the equation of the tangent at the point.