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A line passing through the point $A (9, 0)$ makes an angle of $30 °$ with the positive direction of $x$ -axis. If this line is rotated about $A$ through an angle of $15 °$ in the clockwise direction, then its equation in the new position is

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Important Questions on Point and Straight Line

HARD

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and its Equations

The point

(2, 1)

is translated parallel to the line

L : x - y = 4

2 \sqrt{3}

units. If the new point

Q

lies in the third quadrant, then the equation of the line passing through

Q

and perpendicular to

L

HARD

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and its Equations

The tangent to the curve

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

, parallel to the line

2 y = 4 x + 1

, also passes through the point :

MEDIUM

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and its Equations

Two sides of a rhombus are along the lines,

x - y + 1 = 0

and

7 x - y - 5 = 0

. If its diagonals intersect at

(- 1, - 2)

, then which one of the following is a vertex of this rhombus ?

EASY

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and its Equations

The

y

-intercept of the line passing through

A (6, 1)

and perpendicular to the line

x - 2 y = 4

is …

EASY

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and its Equations

If a straight line passing through the point

P (- 3, 4)

is such that its intercepted portion between the coordinate axes is bisected at

P

, then its equation is :

EASY

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and its Equations

Lines are drawn parallel to the line

4 x - 3 y + 2 = 0,

at a distance

\frac{3}{5}

units from the origin. Then which one of the following points lies on any of these lines?

MEDIUM

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and its Equations

The equation of perpendicular bisectors of sides

A B

and

A C

of a

∆ A B C

are

x - y + 5 = 0

and

x + 2 y = 0

respectively. If the coordinates of vertex

A

are

(1, - 2),

then equation of

B C

EASY

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and its Equations

The equation of the line passing through the point

(- 3, 7)

with slope zero is

HARD

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and its Equations

O (0, 0), A (1, 2), B (3, 4)

are the vertices of

∆ O A B .

The joint equation of the altitude and median drawn from

O

EASY

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and its Equations

The equation of the line passing through

(a, b)

and parallel to the line

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

HARD

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and its Equations

The equation of a straight line which passes through the point

(a \cos^{3} θ, a \sin^{3} θ)

and perpendicular to

x secθ + y c o s e c θ = a

HARD

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and its Equations

Let

L

be the line passing through the point

P (1, 2)

such that its intercepted segment between the co-ordinate axes is bisected at

P

. If

L_{1}

is the line perpendicular to

L

and passing through the point

(- 2, 1)

, then the point of intersection of

L

and

L_{1}

EASY

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and its Equations

Find the y-intercept of the line joining two points

(1, 3)

and

(3, 5)

EASY

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and its Equations

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:

EASY

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and its Equations

If the tangent at the point

P

on the circle

x^{2} + y^{2} + 6 x + 6 y = 2

meets

the

straight

line

5 x - 2 y + 6 = 0

at a point

Q

on the

Y

-axis, then the length of

P Q

EASY

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and its Equations

Line joining the points

(0, 3)

and

(5, - 2)

is a tangent to the curve

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

, then

MEDIUM

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and its Equations

If the perpendicular bisector of the line segment joining the points

P (1, 4)

and

Q (k, 3)

has

y

-intercept equal to

- 4

, then a value of

k

is;

MEDIUM

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and its Equations

Let

b, d > 0

. The locus of all points

P (r, θ)

for which the line

O P

(where

O

is the origin) cuts the line

r \sin θ = b

Q

such that

P Q = d

HARD

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and its Equations

Let

P S

be the median of the triangle with vertices

P (2, 2), Q (6, - 1)

and

R (7, 3)

. The equation of the line passing through

(1, - 1)

and parallel to

P S

MEDIUM

Mathematics>Coordinate Geometry>Point and Straight Line>Straight Line and its Equations

Two vertices of a triangle are

(0, 2)

and

(4, 3) .

If its orthocenter is at the origin, then its third vertex lies in which quadrant?

A line passing through the point A(9,0) makes an angle of 30° with the positive direction of x-axis. If this line is rotated about A through an angle of 15° in the clockwise direction, then its equation in the new position is

Important Questions on Point and Straight Line

Learn and Prepare for any exam you want !

A line passing through the point $A (9, 0)$ makes an angle of $30 °$ with the positive direction of $x$ -axis. If this line is rotated about $A$ through an angle of $15 °$ in the clockwise direction, then its equation in the new position is