Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 55

EASY

JEE Main

IMPORTANT

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The vertex of the parabola bisects the sub-tangent of a point on it in the ratio

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Important Questions on Conic Section

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 56

From the point where any normal to the parabola

y^{2} = 4 a x,

meets the axis, is drawn a line perpendicular to the normal, this line touches a parabola having latus rectum

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 57

The locus of the points of trisection of the double ordinates of the parabola $y^{2} = 4 a x$ is

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JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 58

If the tangents at points

P

and

Q

of the parabola

y^{2} = 4 a x

meet at

R

and

b, c, d

be the lengths of perpendiculars from

P, Q, R

to any tangent to the parabola, then the roots of equation

b x^{2} + 2 d x + c = 0

are necessarily

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 59

A normal chord of a parabola which subtends a right angle at the vertex makes with

x

-axis an angle

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 60

If the normals at two points of the parabola

y^{2} = 4 a x

, meet on the parabola and make angles

α

and

β

with positive direction of x-axis , then

\tan α \tan β =

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 61

If normals at two points

A (x_{1}, y_{1})

and

B (x_{2}, y_{2})

of the parabola

y^{2} = 4 a x,

intersect on the parabola, then

y_{1}, 2 \sqrt{2} a, y_{2}

are in

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 62

If the normals at two points

P

and

Q

of a parabola

y^{2} = 4 a x,

intersect on the parabola, then the line

PQ

passes through the fixed point

HARD

JEE Main

IMPORTANT

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

The normals at the extremities of a chord

PQ

of the parabola

y^{2} = 4 a x

meet on the parabola, then locus of the middle point of

PQ

is