Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 19

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JEE Main

IMPORTANT

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If $(α, β)$ is the foot of perpendicular from $(x_{1}, y_{1})$ to line $l x + m y + n = 0$ , then

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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 20

The integral values of

β

so that point

(0, β)

lies on or inside the triangle having sides

y + 3 x + 2 = 0, 3 y - 2 x - 5 = 0

and

4 y + x - 14 = 0

may be

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

The equation of two equal sides

A B

and

A C

of an isosceles triangle

A B C

are

x + y = 5

and

7 x - y = 3

respectively. If area of

∆ A B C

is

5

square units, then equation of

B C

may be

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JEE Main

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

Two equal sides of an isosceles triangle are the lines

(a + b) x + (a - b) y - 2 a b = 0

and

(a - b) x + (a + b) y - 2 a b = 0

. If the third side passes through the point

(b - a, a - b)

, then the equation of third side may be

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JEE Main

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 1

A line intersects

x

-axis at

A (7, 0)

and

y

-axis at

B (0, - 5)

. A variable line

P Q

which is perpendicular to

A B

intersects

x

-axis at

P

and

y

-axis at

Q

. If the locus of point of intersection of

A Q

and

B P

is

x^{2} + y^{2} + a x + b y + c = 0

, then

a^{2} + b^{2} + c^{2} =

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 2

A straight line

l

passes through a fixed point

(6, 8)

. If locus of the foot of perpendicular on line

l

from origin is a circle, then radius of this circle is .....

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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 3

A line

a x - 3 y + c = 0

is such that its segment between the lines

5 x - y + 4 = 0

and

3 x + 4 y - 4 = 0

is bisected at

(1, 5)

, then the value of

a - c

is .....

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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 5

A line

4 x + y = 1

through the point

A (2, - 7)

meets the line

B C

whose equation is

3 x - 4 y + 1 = 0

at point

B

. If the equation of line

A C

so that

A B = B C

is

a x + 89 y + c = 0

Then

a + c = \dots . .

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 6

Let

A B

be a line segment of length

4

with

A

on the line

y = 2 x

and

B

on the line

y = x

. If the locus of the mid-point of all such line segments is

a x^{2} + b y^{2} + c x y - 4 = 0

.
Then

c^{2} =