Mathematics Crash Course MHT-CET>Chapter 5 - Straight Line>Exercise 1>Q 139

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The point $P (a, b)$ lies on the straight line $3 x + 2 y = 13$ and the point $Q (b, a)$ lies on the straight line $4 x - y = 5,$ then the equation of the line $P Q$ is

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Important Questions on Straight Line

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Mathematics Crash Course MHT-CET>Chapter 5 - Straight Line>Exercise 1>Q 140

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?

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Mathematics Crash Course MHT-CET>Chapter 5 - Straight Line>Exercise 1>Q 141

If

f (α) = x \cos α + y \sin α - p (α)

, then the lines

f (α) = 0

and

f (β) = 0

are perpendicular to each other, if

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Mathematics Crash Course MHT-CET>Chapter 5 - Straight Line>Exercise 1>Q 142

The coordinates of three consecutive vertices of a parallelogram are

(1, 3), (- 1, 2)

and

(2, 5) .

The coordinates of the fourth vertex are

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Mathematics Crash Course MHT-CET>Chapter 5 - Straight Line>Exercise 1>Q 143

If

a, b, c

are in harmonic progression, then straight line

\frac{x}{a} + \frac{y}{b} + \frac{1}{c} = 0

always passes through a fixed point, that point is

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Mathematics Crash Course MHT-CET>Chapter 5 - Straight Line>Exercise 1>Q 144

If the line

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

passes through the points

(2, - 3)

and

(4, - 5),

then

(a, b) =

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Mathematics Crash Course MHT-CET>Chapter 5 - Straight Line>Exercise 1>Q 145

The distance of the line

2 x - 3 y = 4

from the point

(1, 1)

measured parallel to the line

x + y = 1

is

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Mathematics Crash Course MHT-CET>Chapter 5 - Straight Line>Exercise 1>Q 146

Let $α$ be the distance between the lines $- x + y = 2$ and $x - y = 2$ and $β$ be the distance between the lines $4 x - 3 y = 5$ and $6 y - 8 x = 1$ , then

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Mathematics Crash Course MHT-CET>Chapter 5 - Straight Line>Exercise 1>Q 147

For the lines

2 x + 5 y = 7

and

2 x - 5 y = 9,

which of the following statement is true?