The Straight Lines — MATHS STD 11 Science — Question
Gujarat BoardEnglish MediumSTD 11 ScienceMATHSThe Straight Lines2 Marks
Question
Reduce the equation $\sqrt{3}\text{x}+\text{y}+2=0$ to: The normal form and find p and $\alpha.$
✓
Answer
Normal form $(\text{x}\cos\alpha+\text{y}\sin\alpha=\text{p})$$\sqrt3\text{x}+\text{y}+2=0$
$\Rightarrow-\sqrt3\text{x}-\text{y}=2$
$\Rightarrow\Big(\frac{-\sqrt3}{2}\Big)\text{x}+\Big(\frac{-1}{2}\Big)\text{y}=1 $
$\Rightarrow\cos\alpha=\frac{-\sqrt3}{2}=\cos210^\circ$ and $\sin\alpha=\frac{-1}{2}=\sin210^\circ$
$\Rightarrow\text{p}=1,\ \alpha=210^\circ$
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