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

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JEE Main

IMPORTANT

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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

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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 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

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JEE Main

IMPORTANT

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

If a circle intersects the parabola

y^{2} = 4 a x,

at points

A (a t_{1}^{2}, 2 a t_{1}), B (a t_{2}^{2}, 2 a t_{2}), C (a t_{3}^{2}, 2 a t_{3}), D (a t_{4}^{2}, 2 a t_{4})

then

t_{1} + t_{2} + t_{3} + t_{4} =

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JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 65

If the

4^{th}

term in the expansion of

{(p x + \frac{1}{x})}^{n}, n \in N

is

\frac{5}{2}

and three normals to the parabola

y^{2} = x

are drawn through a point

(q, 0),

then

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JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 66

The line

x + y = a

touches the parabola

y = x - x^{2}

and

f (x) = \sin^{2} x + \sin^{2} (x + \frac{π}{3}) + \cos x \cos (x + \frac{π}{3}), g (\frac{5}{4}) = 1, b = (g o f) (x),

then

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JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 67

The coordinates of the point on the parabola

y^{2} = 8 x

which is at a minimum distance from the circle

x^{2} + {(y + 6)}^{2} = 1

are

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JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 68

If the normal at three points $(a p^{2}, 2 a p), (a q^{2}, 2 a q)$ and $(a r^{2}, 2 a r)$ of parabola $y^{2} = 4 a x$ are concurrent, then the common root of equations $p x^{2} + q x + r = 0$ and $a (b - c) x^{2} + b (c - a) x + c (a - b) = 0$ is

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JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 69

If the fourth term in the expansion of

{(\frac{x}{p} + \frac{1}{x})}^{n}, n \in N

is

\frac{5}{2}

and the normal to the parabola

y^{2} = 4 a x,

at

(a t^{2}, 2 a t)

meets the parabola again at

(a T^{2}, 2 a T),

then

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 70

The point on the line

x - y + 2 = 0,

from which the tangent to the parabola

y^{2} = 8 x

is perpendicular to the given line is

(a, b),

then the line

a x + b y + c = 0

is