If a variable line drawn through the intersection of the lines x 3 + y 4 = 1 and x 4 + y 3 = 1 , meets the coordinate axes at A and B , A ≠ B , then the locus of the midpoint of AB is:

14 x + y 2 - 97 x + y + 168 = 0

HARD

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Let a line $L$ pass through the point of intersection of the lines $b x + 10 y - 8 = 0$ and $2 x - 3 y = 0, b \in R - \{\frac{4}{3}\}$ . If the line $L$ also passes through the point $(1, 1)$ and touches the circle $17 (x^{2} + y^{2}) = 16$ , then the eccentricity of the ellipse $\frac{x^{2}}{5} + \frac{y^{2}}{b^{2}} = 1$ is

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Important Questions on Point and Straight Line

MEDIUM

Mathematics>Coordinate Geometry>Point and Straight Line>Family of Lines

If the family of straight lines

a x + b y + c = 0

, where

2 a + 3 b = 4 c

is concurrent at the point

P (l, m)

, then the foot of the perpendicular drawn from

P

to the line

x + y + 1 = 0

EASY

Mathematics>Coordinate Geometry>Point and Straight Line>Family of Lines

If the lines

2 x - 3 y + 5 = 0, 9 x - 5 y + 14 = 0

and

3 x - 7 y + λ = 0

are concurrent, then the value of

λ

is equal to

EASY

Mathematics>Coordinate Geometry>Point and Straight Line>Family of Lines

Consider the set of all lines

p x + q y + r = 0

such that

3 p + 2 q + 4 r = 0 .

Which one of the following statements is true?

HARD

Mathematics>Coordinate Geometry>Point and Straight Line>Family of Lines

If the orthocenter of the triangle formed by the lines

2 x + 3 y - 1 = 0, x + 2 y + 1 = 0

and

a x + b y - 1 = 0

lies at origin, then

\frac{1}{a} + \frac{1}{b} =

EASY

Mathematics>Coordinate Geometry>Point and Straight Line>Family of Lines

Let each of the equations

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

and

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

represent two straight lines passing through the origin. If they have a common line, then the other two lines are given by

MEDIUM

Mathematics>Coordinate Geometry>Point and Straight Line>Family of Lines

The equation of the line passing through the point of intersection of lines

2 x - y + 2 = 0

and

x + y + 4 = 0

and the point

(5, - 2)

EASY

Mathematics>Coordinate Geometry>Point and Straight Line>Family of Lines

If the lines

L_{1} \equiv 2 x + y + 3 = 0, L_{2} \equiv k x + 2 y - 3 = 0

and

L_{3} \equiv 3 x - 2 y + 1 = 0

are concurrent then the cosine of the acute angle between the lines

L_{2} = 0

and

2 x - 5 y + 7 = 0

HARD

Mathematics>Coordinate Geometry>Point and Straight Line>Family of Lines

The line

(K + 1)^{2} x + K y - 2 K^{2} - 2 = 0

passes through a point regardless of the value of

K

. Which of the following is the equation of the line with slope

2

and passing through that point?

MEDIUM

Mathematics>Coordinate Geometry>Point and Straight Line>Family of Lines

Let

C

be the centroid of the triangle with vertices

(3, - 1), (1, 3)

and

(2, 4) .

Let

P

be the point of intersection of the lines

x + 3 y - 1 = 0

and

3 x - y + 1 = 0 .

Then the line passing through the points

C

and

P

also passes through the point

HARD

Mathematics>Coordinate Geometry>Point and Straight Line>Family of Lines

Let

a, b

and

c

be distinct and none of them is equal to

1

. If the lines

x + a y + a = 0

b x + y + b = 0

and

c x + c y + 1 = 0

are concurrent, then the value of

\frac{a}{a - 1} + \frac{b}{b - 1} + \frac{c}{c - 1}

HARD

Mathematics>Coordinate Geometry>Point and Straight Line>Family of Lines

If a variable line drawn through the intersection of the lines

\frac{x}{3} + \frac{y}{4} = 1

and

\frac{x}{4} + \frac{y}{3} = 1

, meets the coordinate axes at

A

and

B

(A \neq B),

then the locus of the midpoint of

AB

is:

MEDIUM

Mathematics>Coordinate Geometry>Point and Straight Line>Family of Lines

Find the equation to the straight line passing through the intersection of the lines

x - 2 y - a = 0

and

x + 3 y - 2 a = 0

and parallel to the straight line

3 x + 4 y = 0

MEDIUM

Mathematics>Coordinate Geometry>Point and Straight Line>Family of Lines

Find the equation of the straight line passing through the intersection of the lines

2 x - 3 y = 10

and

x + 2 y = 6

and the intersection of the lines

16 x - 10 y = 33

and

12 x + 14 y + 29 = 0

HARD

Mathematics>Coordinate Geometry>Point and Straight Line>Family of Lines

Find the equations to the straight lines passing through the point of intersection of the straight lines $A x + B y + C = 0$ and $A^{'} x + B^{'} y + C^{'} = 0$
and

$(i)$ Passing through the origin.

$(i i)$ Parallel to the axis of $y$ .

$(i i i)$ Cutting off a given distance $a$ from the axis of $y$ and

$(i v)$ Passing through the given point $(x^{'}, y^{'})$ .

HARD

Mathematics>Coordinate Geometry>Point and Straight Line>Family of Lines

The straight lines $u_{1} = 0, u_{2} = 0, u_{3} = 0$ and $u_{4} = 0$ Represent sides of a parallelogram as shown in adjacent figure, then-
Question Image

HARD

Mathematics>Coordinate Geometry>Point and Straight Line>Family of Lines

Find equation of the straight line passing through the origin and the point of intersection of

x - y - 4 = 0

and

7 x + y + 20 = 0

. Also prove that it bisects the angle between given lines.

EASY

Mathematics>Coordinate Geometry>Point and Straight Line>Family of Lines

Find the equation to the straight line passing through the intersection of the lines

x + 2 y + 3 = 0

and

3 x + 4 y + 7 = 0

and perpendicular to the straight line

y - x = 8

HARD

Mathematics>Coordinate Geometry>Point and Straight Line>Family of Lines

The equation of the straight line perpendicular to the straight line

3 x + 2 y = 0

and passing through. the point of intersection of the lines

x + 3 y - 1 = 0

and

x - 2 y + 4 = 0

MEDIUM

Mathematics>Coordinate Geometry>Point and Straight Line>Family of Lines

a^{3} - 8 b^{3} - 27 c^{3} = 6 a^{2} b - 12 a b^{2},

then the family of lines

c x + b y + a = 0

are concurrent at

HARD

Mathematics>Coordinate Geometry>Point and Straight Line>Family of Lines

Among the lines passing through

C (3, 1),

B A

is farthest from the origin and cuts the

x

-axis and

y

-axis at

A

and

B

respectively. Then

\frac{B C}{C A}

is....

Let a line L pass through the point of intersection of the lines bx+10y-8=0 and 2x-3y=0,b∈R-43. If the line L also passes through the point 1,1 and touches the circle 17x2+y2=16, then the eccentricity of the ellipse x25+y2b2=1 is

Important Questions on Point and Straight Line

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