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If $l$ denotes the semi-latus rectum of the parabola $y^{2} = 4 a x$ and $S P$ and $S Q$ denote the segments of any focal chord $P Q$ , $S$ being the focus, then $S P$ , $l$ and $S Q$ are in

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Important Questions on Parabola

MEDIUM

Mathematics>Coordinate Geometry>Parabola>Basics of Parabola

The area of the region (in sq. units), enclosed by the circle

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

which is not common to the region bounded by the parabola

y^{2} = x

and the straight line

y = x

, is

HARD

Mathematics>Coordinate Geometry>Parabola>Basics of Parabola

Let

P (4, - 4)

and

Q (9, 6)

be two points on the parabola,

y^{2} = 4 x

and let

X

be any point on the arc

P O Q

of this parabola, where

O

is the vertex of this parabola, such that the area of

∆ P X Q

is maximum. Then this maximum area (in sq. units) is :

HARD

Mathematics>Coordinate Geometry>Parabola>Basics of Parabola

y = m x + c

is the normal at a point on the parabola

y^{2} = 8 x

whose focal distance is

8

units, then

|c|

is equal to:

EASY

Mathematics>Coordinate Geometry>Parabola>Basics of Parabola

If the parabola

x^{2} = 4 a y

passes through the point

(2, 1)

, then the length of the latus rectum is

HARD

Mathematics>Coordinate Geometry>Parabola>Basics of Parabola

If the tangents and normals at the extremities of a focal chord of a parabola intersect at

(x_{1}, y_{1})

and

(x_{2}, y_{2})

respectively, then

MEDIUM

Mathematics>Coordinate Geometry>Parabola>Basics of Parabola

The equation

y^{2} + 3 = 2 (2 x + y)

represents a parabola with the vertex at

MEDIUM

Mathematics>Coordinate Geometry>Parabola>Basics of Parabola

Let

A (4, - 4)

and

B (9, 6)

be points on the parabola,

y^{2} = 4 x .

Let

C

be chosen on the arc

A O B

of the parabola, where

O

is the origin, such that the area of

Δ A C B

is maximum. Then, the area (in sq. units) of

Δ A C B

, is:

EASY

Mathematics>Coordinate Geometry>Parabola>Basics of Parabola

The focus of the curve

y^{2} + 4 x - 6 y + 13 = 0

HARD

Mathematics>Coordinate Geometry>Parabola>Basics of Parabola

Let

E

denote the parabola

y^{2} = 8 x .

Let

P = (- 2, 4)

, and let

Q

and

Q^{'}

be two distinct points on

E

such that the lines

P Q

and

P Q^{'}

are tangents to

E

. Let

F

be the focus of

E

. Then which of the following statements is (are) TRUE?

MEDIUM

Mathematics>Coordinate Geometry>Parabola>Basics of Parabola

The focus of the parabola

y = 2 x^{2} + x

EASY

Mathematics>Coordinate Geometry>Parabola>Basics of Parabola

The two ends of a latus rectum of a parabola are

(5, 8)

and

(- 7, 8)

. Then its focus is

MEDIUM

Mathematics>Coordinate Geometry>Parabola>Basics of Parabola

Let

A (1, 2), B (4, - 4), C (2, 2 \sqrt{2})

be points on the parabola

y^{2} = 4 x .

α

and

β

respectively represent the area of

Δ A B C

and the area of the triangle formed by the tangents at

A, B, C

to the above parabola, then

α β =

HARD

Mathematics>Coordinate Geometry>Parabola>Basics of Parabola

Equation of the directrix of the parabola whose focus is

(0, 0)

and the tangent at the vertex is

x - y + 1 = 0

MEDIUM

Mathematics>Coordinate Geometry>Parabola>Basics of Parabola

The area (in sq. units) of an equilateral triangle inscribed in the parabola

y^{2} = 8 x,

with one of its vertices on the vertex of this parabola is

HARD

Mathematics>Coordinate Geometry>Parabola>Basics of Parabola

The equation of the lines joining the vertex of the parabola

y^{2} = 6 x

to the point on it which have abscissa

24

are

EASY

Mathematics>Coordinate Geometry>Parabola>Basics of Parabola

The cartesian co-ordinates of the point on the parabola

y^{2} = - 16 x,

whose parameter is

\frac{1}{2}

are

EASY

Mathematics>Coordinate Geometry>Parabola>Basics of Parabola

The parabola having its focus at

(3, 2)

and directrix along the

y

-axis has its vertex at

HARD

Mathematics>Coordinate Geometry>Parabola>Basics of Parabola

Let

O

be the vertex and

Q

be any point on the parabola,

x^{2} = 8 y

. If the point

P

divides the line segment

O Q

internally in the ratio

1 : 3

, then the locus of

P

EASY

Mathematics>Coordinate Geometry>Parabola>Basics of Parabola

If the three normals drawn to the parabola,

y^{2} = 2 x

pass through the point

(a, 0), a \neq 0

, then

a

must be greater than :

MEDIUM

Mathematics>Coordinate Geometry>Parabola>Basics of Parabola

Suppose

O A B C

is a rectangle in the

x y

-plane where

O

is the origin and

A, B

lie on the parabola

y = x^{2} .

Then

C

must lie on the curve-

If l denotes the semi-latus rectum of the parabola y2=4ax and SP and SQ denote the segments of any focal chord PQ, S being the focus, then SP, l and SQ are in

Important Questions on Parabola

Learn and Prepare for any exam you want !

If $l$ denotes the semi-latus rectum of the parabola $y^{2} = 4 a x$ and $S P$ and $S Q$ denote the segments of any focal chord $P Q$ , $S$ being the focus, then $S P$ , $l$ and $S Q$ are in