Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 20

EASY

JEE Main

IMPORTANT

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Let $P \equiv (a, b), Q \equiv (c, d)$ and $0 < a < b < c < d, L \equiv (a, 0), M \equiv (c, 0),$ $R$ lies on $x$ -axis such that $PR + RQ$ is minimum, then $R$ divides $LM$ .

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Important Questions on Coordinates and Straight Lines

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JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 21

If

a = \frac{\tan θ}{\tan 3 θ},

then the point

P (a, a^{2})

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 22

If

α

is an integer and

P (α, α^{2})

is a point in the interior of the quadrilateral

x = 0, y = 0, 4 x + y - 21 = 0

and

3 x + y - 4 = 0,

and

(1 + a x)^{n} = 1 + 8 x + 24 x^{2} + \dots,

then

α =

EASY

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 23

If

a, b, c

are variables such that

21 a + 40 b + 56 c = 0

then the family of lines

a x + b y + c = 0

passes through

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JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 24

Consider a triangle

PQR

with

P \equiv (0, 0),

Q \equiv (a, 0),

R \equiv (0, b) .

Then the centroid, orthocentre, and circumcentre

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JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 25

The equation of the line bisecting the obtuse angle between

y - x = 2

and

2 y + x = 5

is

EASY

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 26

The line

l_{1} x + m_{1} y + n = 0

and

l_{2} x + m_{2} y + n = 0

will cut the coordinate axes at concyclic points if

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JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 27

If two sides of a triangle are represented by

2 x - 3 y + 4 = 0

and

3 x + 2 y - 3 = 0,

then its orthocentre lies on the line:

EASY

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 28

Equation of the line equidistant from

3 x + 4 y - 25 = 0

and

3 x + 4 y + 25 = 0

is