HARD

JEE Main

IMPORTANT

Earn 100

The algebraic sum of distances of the line $a x + b y + 2 = 0$ from $(1, 2), (2, 1)$ and $(3, 5)$ is zero and the lines $b x - a y + 4 = 0$ and $3 x + 4 y + 5 = 0$ cut the coordinate axes at concyclic points. Then

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Important Questions on Straight Lines

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 2 - Straight Lines>DPP>Q 6

The equation of the line which is equally inclined to the axes and passes through common points of a family of lines

4 a c x + y (a b + b c + c a - a b c) + a b c = 0

where

a, b, c > 0

are in

H . P .

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 2 - Straight Lines>DPP>Q 7

The base

B C

of a triangle

A B C

is bisected at the point

(p, q)

and the equations of the sides

A B

and

A C

are

p x + q y = 1

and

q x + p y = 1

, respectively. The equation of the median through

A

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 2 - Straight Lines>DPP>Q 8

A (x_{1}, y_{1}), B (x_{2}, y_{2})

and

C (x_{3}, y_{3})

are three vertices of a triangle

A B C .

l x + m y + n = 0

is the equation of a line

L .

If the centroid of the triangle

A B C

is at the origin and algebraic sum of the lengths of the perpendiculars from the vertices of the triangle

A B C

to the line

L

is equal to

1,

then the sum of the squares of reciprocals of the intercepts made by

L

on the coordinate axes is equal to

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 2 - Straight Lines>DPP>Q 9

A straight line passes through the point of intersection of

x - 2 y - 2 = 0

and

2 x - b y - 6 = 0

and the origin, then the complete set of values of

b

for which the acute angle between this line and

y = 0

is less than

45^{°}

, is

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 2 - Straight Lines>DPP>Q 10

The locus of the foot of the perpendicular from the origin on each member of the family

(4 a + 3) x - (a + 1) y - (2 a + 1) = 0

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 2 - Straight Lines>DPP>Q 11

Equation of the diagonals of a rectangle are

y + 8 x - 17 = 0

and

y - 8 x + 7 = 0 .

If the area of the rectangle is

8

sq. units, then the equation of the sides of the rectangle is/are

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 2 - Straight Lines>DPP>Q 12

6 a^{2} - 3 b^{2} - c^{2} + 7 a b - a c + 4 b c = 0

, then the family of lines

a x + b y + c = 0, | a | + | b | \neq 0

is concurrent at

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 2 - Straight Lines>DPP>Q 13

If graph of

x y = 1

is reflected in

y = 2 x

to give the graph

12 x^{2} + r x y + s y^{2} + t = 0,

then

The algebraic sum of distances of the line ax+by+2=0 from (1, 2), (2, 1) and (3, 5) is zero and the lines bx-ay+4=0 and 3x+4y+5=0 cut the coordinate axes at concyclic points. Then

Important Questions on Straight Lines

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The algebraic sum of distances of the line $a x + b y + 2 = 0$ from $(1, 2), (2, 1)$ and $(3, 5)$ is zero and the lines $b x - a y + 4 = 0$ and $3 x + 4 y + 5 = 0$ cut the coordinate axes at concyclic points. Then