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Home » Find the equation of a line for which (i) p = 5, α = 60° (ii) p = 4, α = 150°
Find the equation of a line for which (i) p = 5, α = 60° (ii) p = 4, α = 150°
CBSE | Class 11 | Exercise 23.7 | Maths | RD Sharma | Straight Lines
Find the equation of a line for which (i) p = 5, α = 60° (ii) p = 4, α = 150°

    \[\left( \mathbf{i} \right)~p\text{ }=\text{ }5,\text{ }\alpha \text{ }=\text{ }60{}^\circ \]

Given:

    \[p\text{ }=\text{ }5,\text{ }\alpha \text{ }=\text{ }60{}^\circ \]

The equation of the line in normal form is given by

On using the formula,

    \[x\text{ }cos~\alpha \text{ }+\text{ }y\text{ }sin\text{ }\alpha \text{ }=\text{ }p\]

Now, putting, we get

    \[x\text{ }cos\text{ }60{}^\circ \text{ }+\text{ }y\text{ }sin\text{ }60{}^\circ \text{ }=\text{ }5\]

    \[x/2\text{ }+~\surd 3y/2\text{ }=\text{ }5\]

    \[x\text{ }+\text{ }\surd 3y\text{ }=\text{ }10\]

∴ The equation of line in normal form is:

    \[~x\text{ }+\text{ }\surd 3y\text{ }=\text{ }10.\]

    \[\left( \mathbf{ii} \right)~p\text{ }=\text{ }4,\text{ }\alpha \text{ }=\text{ }150{}^\circ \]

Given:

    \[p\text{ }=\text{ }4,\text{ }\alpha \text{ }=\text{ }150{}^\circ \]

The equation of the line in normal form is given by

On using the formula,

    \[x\text{ }cos~\alpha \text{ }+\text{ }y\text{ }sin\text{ }\alpha \text{ }=\text{ }p\]

Now, putting the values, we have,

    \[x\text{ }cos\text{ }150{}^\circ \text{ }+\text{ }y\text{ }sin\text{ }150{}^\circ \text{ }=\text{ }4\]

    \[cos\text{ }\left( 180{}^\circ ~\text{ }\theta \right)\text{ }=\text{ }\text{ }cos\text{ }\theta \text{ },\]

    \[sin\text{ }\left( 180{}^\circ ~\text{ }\theta \right)\text{ }=\text{ }sin\text{ }\theta \]

or,

    \[x\text{ }cos\left( 180{}^\circ ~\text{ }30{}^\circ \right)\text{ }+\text{ }y\text{ }sin\left( 180{}^\circ ~\text{ }30{}^\circ \right)\text{ }=\text{ }4\]

    \[\text{ }x\text{ }cos\text{ }30{}^\circ ~+\text{ }y\text{ }sin\text{ }30{}^\circ ~=\text{ }4\]

Or,

    \[\surd 3x/2\text{ }+\text{ }y/2\text{ }=\text{ }4\]

    \[-\surd 3x\text{ }+\text{ }y\text{ }=\text{ }8\]

∴ The equation of line in normal form is:

    \[~-\surd 3x\text{ }+\text{ }y\text{ }=\text{ }8.\]

 

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