EASY

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The distance between the points $(12, \frac{π}{3})$ and $(9, - \frac{π}{6})$ is?

( Where above coordinates are in the polar coordinate system)

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Important Questions on Straight Lines

EASY

Mathematics>Coordinate Geometry>Straight Lines>Basics of 2D Coordinate Geometry

The equation of the graph shown here is:

Question Image

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Basics of 2D Coordinate Geometry

Find the area of the triangle formed with the three straight lines represented by:

$(i) x + y = 0 (i i) 3 x = 5 y; a n d (i i i) y = 3 x - 12$

HARD

Mathematics>Coordinate Geometry>Straight Lines>Basics of 2D Coordinate Geometry

Find the area of the triangle formed by the lines

x - 3 y = 0, x - y = 4

and

x + y = 4 .

EASY

Mathematics>Coordinate Geometry>Straight Lines>Basics of 2D Coordinate Geometry

A straight line through the origin

O

meets the parallel lines

4 x + 2 y = 9

and

2 x + y + 6 = 0

P

and

Q

respectively. The point

O

divides the segment

P Q

in the ratio

EASY

Mathematics>Coordinate Geometry>Straight Lines>Basics of 2D Coordinate Geometry

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>Straight Lines>Basics of 2D Coordinate Geometry

P (- 3, - 2, 4), Q (- 9, - 8, 10)

and

R (- 5, - 4, 6)

are collinear, then the ratio in which

R

divides

P Q

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Basics of 2D Coordinate Geometry

Find the ratio in which line $3 x + 2 y = 17$ divides the line segment joined by points $(2, 5)$ and $(5, 2) .$

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Basics of 2D Coordinate Geometry

A point

P

moves on the line

2 x - 3 y + 4 = 0 .

Q (1, 4)

and

R (3, - 2)

are fixed points, then the locus of the centroid of

Δ P Q R

is a line:

HARD

Mathematics>Coordinate Geometry>Straight Lines>Basics of 2D Coordinate Geometry

Let

A (1, 0), B (6, 2)

and

C (\frac{3}{2}, 6)

be the vertices of a triangle

A B C .

P

is a point inside the triangle

A B C

such that the triangles

A P C, A P B

and

B P C

have equal areas, then the length of the line segment

P Q,

where

Q

is the point

(- \frac{7}{6}, - \frac{1}{3}),

EASY

Mathematics>Coordinate Geometry>Straight Lines>Basics of 2D Coordinate Geometry

Let

R = {(P, Q) | P

and

Q

are at the same distance from the origin

}

be a relation, then the equivalence class of

(1, - 1)

is the set

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Basics of 2D Coordinate Geometry

Let

x_{0}, y_{0}

be fixed real numbers such that

x_{0}^{2} + y_{0}^{2} > 1

. If

x, y

are arbitrary real numbers such that

x^{2} + y^{2} \leq 1,

then the minimum value of

{(x - x_{0})}^{2} + {(y - y_{0})}^{2}

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Basics of 2D Coordinate Geometry

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>Straight Lines>Basics of 2D Coordinate Geometry

P (8, 10)

and

Q (14, - 2)

are two given points and the point

R

divides the line-segment

P Q

externally in the ratio

8 : 6

. The coordinates of

R

are

HARD

Mathematics>Coordinate Geometry>Straight Lines>Basics of 2D Coordinate Geometry

If the distance between the points

(x, 0)

and

(- 7, 0)

10

. Then, the possible values of

x

are ______.

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Basics of 2D Coordinate Geometry

Locus of the image of the point $(2, 3)$ in the line $(2 x - 3 y + 4) + k (x - 2 y + 3) = 0, k \in R,$ is a

HARD

Mathematics>Coordinate Geometry>Straight Lines>Basics of 2D Coordinate Geometry

Let

B C

be a fixed line segment in the plane. The locus of a point

A

such that the triangle

A B C

is isosceles, is (with finitely many possible exceptional points)

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Basics of 2D Coordinate Geometry

Let

S

be the set of all triangles in the

x y

-plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangle in

S

has area

50

sq. units, then the number of elements in the set

S

is:

EASY

Mathematics>Coordinate Geometry>Straight Lines>Basics of 2D Coordinate Geometry

Locus of the centre of rolling circle in a plane will be

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Basics of 2D Coordinate Geometry

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:

HARD

Mathematics>Coordinate Geometry>Straight Lines>Basics of 2D Coordinate Geometry

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 :

The distance between the points 12, π3 and 9, -π6 is? ( Where above coordinates are in the polar coordinate system)

Important Questions on Straight Lines

Learn and Prepare for any exam you want !

The distance between the points $(12, \frac{π}{3})$ and $(9, - \frac{π}{6})$ is?

( Where above coordinates are in the polar coordinate system)