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Equation of chord of the parabola $y^{2} = 16 x$ whose mid point is $(1, 1)$ , is

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Important Questions on Parabola

MEDIUM

Mathematics>Coordinate Geometry>Parabola>Parabola and a Line

If the

x

-intercept of a focal chord of the parabola

y^{2} = 8 x + 4 y + 4

3

, then the length of this chord is equal to _____ .

EASY

Mathematics>Coordinate Geometry>Parabola>Parabola and a Line

The condition that the straight line

l x + m y + n = 0

touches the parabola

x^{2} = 4 a y

MEDIUM

Mathematics>Coordinate Geometry>Parabola>Parabola and a Line

Let

P_{1}

be a parabola with vertex

(3, 2)

and focus

(4, 4)

and

P_{2}

be its mirror image with respect to the line

x + 2 y = 6

. Then the directrix of

P_{2}

x + 2 y =

_____.

HARD

Mathematics>Coordinate Geometry>Parabola>Parabola and a Line

If a chord, which is not a tangent, of the parabola

y^{2} = 16 x

has the equation

2 x + y = p

, and midpoint

(h, k)

, then which of the following is (are) possible value(s) of

p, h

and

k

HARD

Mathematics>Coordinate Geometry>Parabola>Parabola and a Line

Let

P

be a point on the parabola,

y^{2} = 12 x

and

N

be the foot of the perpendicular drawn from

P

, on the axis of the parabola. A line is now drawn through the mid-point

M

P N

, parallel to its axis which meets the parabola at

Q

. If the

y -

intercept of the line

NQ

\frac{4}{3},

then :

MEDIUM

Mathematics>Coordinate Geometry>Parabola>Parabola and a Line

Let the tangent to the curve

x^{2} + 2 x - 4 y + 9 = 0

at the point

P (1, 3)

on it meet the

y -

axis at

A .

Let the line passing through

P

and parallel to the line

x - 3 y = 6

meet the parabola

y^{2} = 4 x

B .

B

lies on the line

2 x - 3 y = 8,

then

{(A B)}^{2}

is equal to

_______.

EASY

Mathematics>Coordinate Geometry>Parabola>Parabola and a Line

Find the value of

k

if the line

2 y = 5 x + k

is tangent to the parabola

y^{2} = 6 x

HARD

Mathematics>Coordinate Geometry>Parabola>Parabola and a Line

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>Parabola and a Line

The length of the chord of the parabola

y^{2} = 4 a x (a > 0)

which passes through the vertex and makes an acute angle

α

with the axis of the parabola is

EASY

Mathematics>Coordinate Geometry>Parabola>Parabola and a Line

The line

y = 4 x + c

touches the parabola

y^{2} = 4 x

, if

HARD

Mathematics>Coordinate Geometry>Parabola>Parabola and a Line

The tangents to the curve

y = {(x - 2)}^{2} - 1

at its points of intersection with the line

x - y = 3,

intersect at the point:

MEDIUM

Mathematics>Coordinate Geometry>Parabola>Parabola and a Line

The vertices of the base of an isosceles triangle lie on a parabola

y^{2} = 4 x

and the base is a part of the line

y = 2 x - 4

. If the third vertex of the triangle lies on the

x

-axis, its coordinates are

MEDIUM

Mathematics>Coordinate Geometry>Parabola>Parabola and a Line

Let

P (a t^{2}, 2 a t), Q, R (a r^{2}, 2 a r)

be three points on a parabola

y^{2} = 4 a x

. If

P Q

is the focal chord and

P K, Q R

are parallel where the co-ordinates of

K

(2 a, 0),

then the value of

r

MEDIUM

Mathematics>Coordinate Geometry>Parabola>Parabola and a Line

Let

R

be the focus of the parabola

y^{2} = 20 x

and the line

y = m x + c

intersect the parabola at two points

P

and

Q

. Let the points

G (10, 10)

be the centroid of the triangle

P Q R

. If

c - m = 6

, then

P Q^{2}

MEDIUM

Mathematics>Coordinate Geometry>Parabola>Parabola and a Line

Let

P : y^{2} = 4 a x, a > 0

be a parabola with focus

S

.Let the tangents to the parabola

P

make an angle of

\frac{π}{4}

with the line

y = 3 x + 5

touch the parabola

P

A

and

B

. Then the value of

a

for which

A, B

and

S

are collinear is:

MEDIUM

Mathematics>Coordinate Geometry>Parabola>Parabola and a Line

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>Parabola and a Line

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

MEDIUM

Mathematics>Coordinate Geometry>Parabola>Parabola and a Line

Let

C

be the locus of the mirror image of a point on the parabola

y^{2} = 4 x

with respect to the line

y = x

. Then the equation of tangent to

C

P (2, 1)

is :

EASY

Mathematics>Coordinate Geometry>Parabola>Parabola and a Line

The line

y = mx + 2

intersects the parabola

y = {ax}^{2} + 5 x - 2

(1, 5)

. Then the value of

a + m

is equal to

HARD

Mathematics>Coordinate Geometry>Parabola>Parabola and a Line

The length of the chord of the parabola

x^{2} = 4 y

having equation

x - \sqrt{2} y + 4 \sqrt{2} = 0

Equation of chord of the parabola y2=16x whose mid point is (1,1), is

Important Questions on Parabola

Learn and Prepare for any exam you want !

Equation of chord of the parabola $y^{2} = 16 x$ whose mid point is $(1, 1)$ , is