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Home » Find the equation of the straight lines passing through the following pair of points: (i) (0, 0) and (2, -2) (ii) (a, b) and (a + c sin α, b + c cos α)
Find the equation of the straight lines passing through the following pair of points: (i) (0, 0) and (2, -2) (ii) (a, b) and (a + c sin α, b + c cos α)
CBSE | Class 11 | Exercise 23.5 | Maths | RD Sharma | Straight Lines | The Straight Lines
Find the equation of the straight lines passing through the following pair of points: (i) (0, 0) and (2, -2) (ii) (a, b) and (a + c sin α, b + c cos α)

    \[\left( i \right)\text{ }\left( 0,\text{ }0 \right)\text{ }and\text{ }\left( 2,\text{ }-2 \right)\]

Given:

    \[\left( {{x}_{1}},\text{ }{{y}_{1}} \right)\text{ }=\text{ }\left( 0,\text{ }0 \right),~\left( {{x}_{2}},\text{ }{{y}_{2}} \right)\text{ }=\text{ }\left( 2,\text{ }-2 \right)\]

The equation of the line passing through the two points :

    \[\left( 0,\text{ }0 \right)\text{ }and\text{ }\left( 2,\text{ }-2 \right)\]

is

According to formula,

RD Sharma Solutions for Class 11 Maths Chapter 23 – The Straight Lines - image 10

    \[y\text{ }=\text{ }\text{ }x\]

∴ The equation of line is 

    \[y\text{ }=\text{ }-x\]

 

    \[\left( \mathbf{ii} \right)~\left( a,\text{ }b \right)\text{ }and\text{ }\left( a\text{ }+\text{ }c\text{ }sin\text{ }\alpha ,\text{ }b\text{ }+\text{ }c\text{ }cos\text{ }\alpha \right)\]

Given:

    \[\left( {{x}_{1}},\text{ }{{y}_{1}} \right)\]

    \[=\text{ }\left( a,\text{ }b \right),\text{ }\left( {{x}_{2}},\text{ }{{y}_{2}} \right)\]

 

    \[=\text{ }\left( a\text{ }+\text{ }c\text{ }sin\text{ }\alpha ,\text{ }b\text{ }+\text{ }c\text{ }cos\text{ }\alpha \right)\]

hence, the equation of the line passing through the two points:

    \[~\left( 0,\text{ }0 \right)\text{ }and\text{ }\left( 2,\text{ }-2 \right)\]

is,

By using the formula,

RD Sharma Solutions for Class 11 Maths Chapter 23 – The Straight Lines - image 11

    \[y\text{ }\text{ }b\text{ }=\text{ }cot\text{ }\alpha \text{ }\left( x\text{ }\text{ }a \right)\]

∴ The equation of line is:

    \[~y\text{ }\text{ }b\text{ }=\text{ }cot\text{ }\alpha \text{ }\left( x\text{ }\text{ }a \right)\]

i

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