Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 32

HARD

JEE Main

IMPORTANT

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Let $P (α, β)$ be any point on parabola $y^{2} = 4 x, (0 \leq β \leq 2) . M$ is the foot of perpendicular from the focus $S$ to the tangent at $P,$ then the maximum value of area of $Δ P M S =$

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Important Questions on Conic Section

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 33

The point on the parabola

4 x = y^{2} + 9 - 6 y

which is closest to the circle

x^{2} + y^{2} - 10 x - 10 y + 49 = 0

is

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 34

The point

A

on the parabola

y^{2} = 4 a x

for which

|A B - A C|

is maximum, where

B (0, a)

and

C (- a, 0)

is

EASY

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 35

If the circle

x^{2} + y^{2} + λ x = 0, λ \in R

touches the parabola

y^{2} = 16 x

internally, then

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 36

If

P

is the pole of chord

A B

of a parabola and the length of perpendiculars from

A, P, B

on any tangent to the curve be

p_{1}, p_{2}

and

p_{3},

then

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 37

The locus of the point of intersection of normals at the points on the parabola where tangents drawn meet at the directrix is

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 38

The point

(- 2 m, m + 1)

is an interior point of the smaller region bounded by the circle

x^{2} + y^{2} = 4

and parabola

y^{2} = 4 x

. Then,

m

belongs to the interval

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 39

If

(p^{2}, p - 2)

be a point interior to the region of the parabola

y^{2} = 2 x

bounded by the chord joining the points

(2, 2)

and

(8, - 4),

then

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 40

If tangents at

A

and

B

on the parabola

y^{2} = 4 a x

intersect at point

C

, then ordinates of

A, C

and

B

are