Question

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In what follows, p denotes the distance of the straight line from the origin and a denotes the angle
made by the normal ray drawn from the origin to the straight line with Ox measured in the
anti-clockwise sense. Find the equations of the straight lines with the following values of
(1) p = 5, alpha = 60°

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Answer 1

Answer:

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Answer 2

✯ $\textbf{Given:}$ ✯

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$\mathsf{p=5\;\;and\;\;\alpha=60^\circ}$

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✯ $\textbf{To find:}$ ✯

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$\textsf{The equation the given line}$

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✯ $\textbf{Solution:}$ ✯

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$\large\underline{\red{\sf \pink{\bigstar} }}$$\textbf{Formula used:}$ $\large\underline{\red{\sf \pink{\bigstar} }}$

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$\boxed{\begin{minipage}{8cm} \\\underline{\mathsf{Normal\;form\;of\;st.line:}}\\\\\mathsf{x\;cos\alpha+y\;sin\alpha=p}\\\\\mathsf{where,}\\\mathsf{p\;is\;the\;perpendicular\;distance\;of\;the\;line\;from\;origin}\\\mathsf{\alpha\;is\;the\;angle\;made\;by\;the\;perpendicular\;with\;x-axis}\\ \end{minipage}}$

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$\mathsf{Here,\;p=5,\;\alpha=60^\circ}$

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$\large\underline{\red{\sf \red{\bigstar} }}$$\textsf{The required line is}$ $\large\underline{\red{\sf \red{\bigstar} }}$

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$\mathsf{x\;cos\alpha+y\;sin\;\alpha=p}$

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$\mathsf{x\;cos60^\circ+y\;sin60^\circ=5}$

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$\mathsf{x\left(\dfrac{1}{2}\right)+y\;sin\left(\dfrac{\sqrt3}{2}\right)=5}$

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$\mathsf{\dfrac{x}{2}+\dfrac{\sqrt3\,y}{2}=5}$

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$\mathsf{\dfrac{x+\sqrt3\,y}{2}=5}$

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$\mathsf{x+\sqrt3\,y=10}$

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$\implies\boxed{\mathsf{x+\sqrt3\,y-10=0}}$$\large\underline{\red{\sf \orange{\bigstar} }}$

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$\blue{\sf{\star\;Note-}}$

• $\textsf{Kindly views Answer from brainly. in for better understanding the concept used here.}$

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