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If point $(4, 4)$ lies on parabola whose focus lies on $x$ -axis and directrix is $l x + m y = 1$ such that $(l, m)$ lies on curve $x^{2} + y^{2} - 32 x y + 8 x + 8 y - 1 = 0$ then:

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Important Questions on Parabola

MEDIUM

Mathematics>Coordinate Geometry>Parabola>Basics of Parabola

The equation of the latus rectum of a parabola is

x + y = 8

and the equation of the tangent at the vertex is

x + y = 12 .

Then, the length of the latus rectum is

HARD

Mathematics>Coordinate Geometry>Parabola>Basics of Parabola

P Q

be a double ordinate of the parabola,

y^{2} = - 4 x,

where

P

lies in the second quadrant. If

R

divides

P Q

in the ratio

2 : 1,

then the locus of

R

is:

MEDIUM

Mathematics>Coordinate Geometry>Parabola>Basics of Parabola

The directrix of the parabola

2 y^{2} + 25 x = 0

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

MEDIUM

Mathematics>Coordinate Geometry>Parabola>Basics of Parabola

If one end of a focal chord of the parabola,

y^{2} = 16 x

is at

(1, 4)

, then the length of this focal chord is

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 equation

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

represents a parabola with the vertex at

EASY

Mathematics>Coordinate Geometry>Parabola>Basics of Parabola

A parabola

y^{2} = 32 x

is drawn. From its focus, a line of slope

1

is drawn. The equation of the line is

MEDIUM

Mathematics>Coordinate Geometry>Parabola>Basics of Parabola

The equation of the directrix of the parabola

x^{2} - 4 x - 3 y + 10 = 0

EASY

Mathematics>Coordinate Geometry>Parabola>Basics of Parabola

The vertex of the parabola

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

is shifted

p

units to the right and then

q

units up. If the resulting point is

(4, 5),

then the values of

p

and

q

respectively are

EASY

Mathematics>Coordinate Geometry>Parabola>Basics of Parabola

The length of the Latus rectum of the parabola

x = a y^{2} + b y + c

HARD

Mathematics>Coordinate Geometry>Parabola>Basics of Parabola

A chord is drawn through the focus of the parabola

y^{2} = 6 x

such that its distance from the vertex of this parabola is

\frac{\sqrt{5}}{2}

, then its slope can be

EASY

Mathematics>Coordinate Geometry>Parabola>Basics of Parabola

Let a parabola

P

be such that its vertex and focus lie on the positive

x

-axis at a distance

2

and

4

units from the origin, respectively. If tangents are drawn from

O (0, 0)

to the parabola

P

which meet

P

S

and

R

, then the area (in sq. units) of

Δ S O R

is equal to :

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

HARD

Mathematics>Coordinate Geometry>Parabola>Basics of Parabola

An equilateral triangle is inscribed in the parabola

y^{2} = 4 a x,

where one vertex of the triangle is at the vertex of the parabola. The length of the side of the triangle is

MEDIUM

Mathematics>Coordinate Geometry>Parabola>Basics of Parabola

In which of these cases, the parabola generated by the given pair of directrix and focus will be a degenerate case?

HARD

Mathematics>Coordinate Geometry>Parabola>Basics of Parabola

What will be the area of the triangle formed by the lines joining the vertex of the parabola

y^{2} = 28 x

to the ends of its latus rectum?

EASY

Mathematics>Coordinate Geometry>Parabola>Basics of Parabola

The vertex of the parabola

y = (x - 2) (x - 8) + 7

MEDIUM

Mathematics>Coordinate Geometry>Parabola>Basics of Parabola

The centres of those circles which touch the circle,

x^{2} + y^{2} - 8 x - 8 y - 4 = 0,

externally and also touch the

x

- axis, lie on

HARD

Mathematics>Coordinate Geometry>Parabola>Basics of Parabola

Suppose the parabola

{(y - k)}^{2} = 4 (x - h),

with vertex

A

, passes through

O = (0, 0)

and

L = (0, 2) .

Let

D

be an end point of the latus rectum. Let the

y

-axis intersect the axis of the parabola at

P

. Then

∠ P D A

is equal to

If point (4,4) lies on parabola whose focus lies on x-axis and directrix is lx+my=1 such that (l,m) lies on curve x2+y2-32xy+8x+8y-1=0 then:

Important Questions on Parabola

Learn and Prepare for any exam you want !

If point $(4, 4)$ lies on parabola whose focus lies on $x$ -axis and directrix is $l x + m y = 1$ such that $(l, m)$ lies on curve $x^{2} + y^{2} - 32 x y + 8 x + 8 y - 1 = 0$ then: