Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 1 - Coordinate Systems and Coordinates>Multiple Choice I>Q 8

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IMPORTANT

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The locus of a point $P$ which divides the line joining $(1, 0)$ and $(2 \cos θ, 2 \sin θ)$ internally in the ratio $2 : 3$ for all $θ$ , is a

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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 9

The orthocenter, circumcentre, centroid and incentre of the triangle formed by lines

x + y = a

with the coordinate axes lie on :

HARD

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 1 - Coordinate Systems and Coordinates>Multiple Choice I>Q 10

$A$ and $B$ are fixed points. The vertex $C$ of $Δ A B C$ moves such that $\cot A + \cot B =$ constant. The locus of $C$ is a straight line

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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 11

The points with the co-ordinates

(2 a, 3 a), (3 b, 2 b)

and

(c, c)

are collinear

(a, b, c \neq 0)

:

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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 12

A (- 5, 0)

and

B (3, 0)

are two vertices of a triangle

A B C

. Its area is

20 {cm}^{2}

. The vertex

C

lies on the line

x - y = 2

, then the vertex

C

are :

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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 14

If the equation of the locus of a point equidistant from the points

(a_{1}, b_{1})

and

(a_{2}, b_{2})

is

(a_{1} - a_{2}) x + (b_{1} - b_{2}) y + c = 0

, then the value of

c

is

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 1 - Coordinate Systems and Coordinates>Multiple Choice I>Q 15

If the point

(x_{1} + t (x_{2} - x_{1}), y_{1} + t (y_{2} - y_{1}))

divides the join of

(x_{1}, y_{1})

and

(x_{2}, y_{2})

internally, then

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 1 - Coordinate Systems and Coordinates>Multiple Choice I>Q 16

If

P (1, 2), Q (4, 6), R (5, 7)

and

S (a, b)

are the vertices of a parallelogram

P Q R S,

then -

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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 17

If the sum of the distances of a point from two perpendicular lines in the plane is

1

, then its locus is :