Let a and b be any two numbers satisfying 1 a 2 + 1 b 2 = 1 4 . Then, the foot of perpendicular from the origin on the variable line x a + y b = 1 lies on :

A hyperbola with each semi-axis = 2 .

A hyperbola with each semi-axis = 2

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The extremities of a diagonal of a parallelogram are the points $(3, - 4)$ and $(- 6, 5)$ . If third vertex is $(- 2, 1)$ , then fourth vertex is -

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Important Questions on Point and Straight Line

MEDIUM

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and a Point

A point on the straight line,

3 x + 5 y = 15

which is equidistant from the coordinate axes will lie only in:

HARD

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and a Point

Let

a

and

b

be any two numbers satisfying

\frac{1}{a^{2}} + \frac{1}{b^{2}} = \frac{1}{4} .

Then, the foot of perpendicular from the origin on the variable line

\frac{x}{a} + \frac{y}{b} = 1

lies on :

HARD

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and a Point

2 x - y + 1 = 0

is a tangent to the hyperbola

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{16} = 1

, then which of the following CANNOT be sides of a right angled triangle?

EASY

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and a Point

The length of the perpendicular from the origin, on normal to the curve,

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

, at the point

(2, 2)

, is.

HARD

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and a Point

If a circle of radius

R

passes through the origin

O

and intersects the coordinate axes at

A

and

B

, then the locus of the foot of perpendicular from

O

A B

is :

HARD

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and a Point

Let two points be

A (1, - 1)

and

B (0, 2) .

If a point

P (x^{'}, y^{'})

be such that the area of

∆ P A B = 5

sq. units and it lies on the line

3 x + y - 4 λ = 0,

then a value of

λ

EASY

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and a Point

A straight line through a fixed point

(2, 3)

intersects the coordinate axes at distinct points

P

and

Q

. If

O

is the origin and the rectangle

O P R Q

is completed, then the locus of

R

is:

MEDIUM

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and a Point

A ray of light coming from the point $(2, 2 \sqrt{3})$ is incident at an angle $30 °$ on the line $x = 1$ at the point $A$ . The ray gets reflected on the line $x = 1$ and meets $x$ -axis at the point $B$ . Then, the line $A B$ passes through the point

MEDIUM

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and a Point

Two sides of a parallelogram are along the lines,

x + y = 3

and

x - y + 3 = 0 .

If its diagonals intersect at

(2, 4),

then one of its vertex is:

MEDIUM

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and a Point

If the sum of distances from a point

P

on two mutually perpendicular straight lines is

1

unit, then the locus of

P

EASY

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and a Point

The reflection of the point

(α, β, γ)

in the

x y -

plane is

HARD

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and a Point

For $a > b > c > 0$ , the distance between $(1, 1)$ and the point of intersection of the lines $a x + b y + c = 0$ and $b x + a y + c = 0$ is less than $2 \sqrt{2}$ . Then

MEDIUM

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and a Point

The set of all possible values of

θ

in the interval

(0, π)

for which the points

(1, 2)

and

(\sin θ, \cos θ)

lie on the same side of the line

x + y = 1

is?

EASY

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and a Point

Suppose that the points

(h, k), (1, 2)

and

(- 3, 4)

lie on the line

L_{1} .

If a line

L_{2}

passing through the points

(h, k)

and

(4, 3)

is perpendicular to

L_{1},

then

\frac{k}{h}

equals:

MEDIUM

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and a Point

Let

L

denote the line in the

x y

-plane with

x

and

y

intercepts as

3

and

1

respectively. Then the image of the point

(- 1, - 4)

in the line is :

EASY

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and a Point

The foot of the perpendicular drawn from the point

(1, 8, 4)

on the line joining the point

(0, - 11, 4)

and

(2, - 3, 1)

EASY

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and a Point

The polar coordinate of a point

P

(2, - \frac{π}{4}) .

The polar coordinate of the point

Q

which is such that line joining

P Q

is bisected perpendicularly by the initial line, is

MEDIUM

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and a Point

Let

C

be the circle with centre

(0, 0)

and radius

3 unit

. The equation of the locus of the mid points of the chords of the circle

C

that subtend an angle of

\frac{2 π}{3}

at its centre, is:

EASY

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and a Point

A line has slope

m

and

y

-intercept 4. The distance between the origin and the line is equal to

HARD

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and a Point

The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices

(0, 0), (0, 41)

and

(41, 0)

The extremities of a diagonal of a parallelogram are the points 3, - 4 and -6, 5 . If third vertex is - 2, 1 , then fourth vertex is -

Important Questions on Point and Straight Line

Learn and Prepare for any exam you want !

The extremities of a diagonal of a parallelogram are the points $(3, - 4)$ and $(- 6, 5)$ . If third vertex is $(- 2, 1)$ , then fourth vertex is -