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IMPORTANT

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If the distance of any point $(x, y)$ from the origin is defined as $d (x, y) = \max \{|x|, |y|\}, where d (x, y) = a$ a non zero constant, then the locus is

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Important Questions on Coordinate Systems and Coordinates

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JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 1 - Coordinate Systems and Coordinates>Multiple Choice I>Q 22

The points

(α, β), (γ, δ), (α, δ)

and

(γ, β)

taken in order, where

α, β, γ, δ

are different real numbers, are

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JEE Main/Advanced

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 1 - Coordinate Systems and Coordinates>Multiple Choice I>Q 23

The cartesian co-ordinates

(x, y)

of a point on a curve are given by

x : y : 1 = t^{3} : t^{2} - 3 : t - 1

where

t

is a parameter, then the points given by

t = a, b, c

are collinear, if

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JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 1 - Coordinate Systems and Coordinates>Multiple Choice I>Q 25

If the square

A B C D

where

A (0, 0), B (2, 0), C (2, 2)

and

D (0, 2)

undergoes the following three transformations successively
(i)

f_{1} (x, y) \to (y, x)

(ii)

f_{2} (x, y) \to (x + 3 y, y)

(iii)

f_{3} (x, y) \to (\frac{x - y}{2}, \frac{x + y}{2})

then the final figure is a :

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 1 - Coordinate Systems and Coordinates>Multiple Choice I>Q 26

If the points

(- 2, 0), (- 1, \frac{1}{\sqrt{3}})

and

(\cos θ, \sin θ)

are collinear, then the number of values of

θ \in [0, 2 π]

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 1 - Coordinate Systems and Coordinates>Multiple Choice I>Q 27

$A B C$ is an equilateral triangle such that the vertices $B$ and $C$ lie on two parallel lines at a distance $6$ . If $A$ lies between the parallel lines at a distance $4$ from one of them, then the length of a side of the equilateral triangle is

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IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 1 - Coordinate Systems and Coordinates>Multiple Choice I>Q 28

Without changing the direction of co-ordinate axes, origin is transferred to

(h, k)

so that the linear (one degree) terms in

x^{2} + y^{2} - 4 x + 6 y - 7 = 0

are eliminated. Then the point

(h, k)

is :

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JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 1 - Coordinate Systems and Coordinates>Multiple Choice I>Q 29

A B C D

is a square whose vertices

A, B, C

and

D

are

(0, 0), (2, 0), (2, 2)

and

(0, 2)

respectively. This square is rotated in the

X - Y

plane with an angle of

30 °

in anticlockwise direction about an axis passing through the vertex

A

the equation of the diagonal

B D

of this rotated square is......... If

E

is the centre of the square, the equation of the circumcircle of the triangle

A B E

is :

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JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 1 - Coordinate Systems and Coordinates>Multiple Choice I>Q 30

t_{1}, t_{2}

and

t_{3}

are distinct, the points

(t_{1}, 2 a t_{1} + a t_{1}^{3}), (t_{2}, 2 a t_{2} + a t_{2}^{3})

and

(t_{3}, 2 a t_{3} + a t_{3}^{3})

are collinear, if :

If the distance of any point x,y from the origin is defined as dx,y=maxx,y,where dx,y=a a non zero constant, then the locus is

Important Questions on Coordinate Systems and Coordinates

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If the distance of any point $(x, y)$ from the origin is defined as $d (x, y) = \max \{|x|, |y|\}, where d (x, y) = a$ a non zero constant, then the locus is