Question

Find the equation of the line which passes through (1,under-root3) and makes an angle 30^0 with the line x - under-root3*y + under-root3 = 0.

Answer 1

Answer on Question #45085 – Math - Analytic Geometry

Problem.

Find the equation of the line which passes through (1, under-root3) and makes an angle $30^{\wedge}0$ with the line $x$ - under-root3*$y$ + under-root3 = 0.

Solution.

The slope of line $x - \sqrt{3}y + \sqrt{3} = 0$ is $y = \frac{1}{\sqrt{3}}x + 1$ (red line). $\frac{1}{\sqrt{3}} = \tan 30{}^\circ$, so the slope of the line which makes an angle $30{}^\circ$ with the line $\tan 0{}^\circ = 0$ or $\tan 30{}^\circ = 0$. Then the new line has equation $y = \sqrt{3}$ (green line) or $y = \sqrt{3}(x - 1) + \sqrt{3} = \sqrt{3}x$ (blue line) (as the both pass through point $A(1, \sqrt{3})$).

Answer: $x = \sqrt{3}$ or $y = \sqrt{3}x$.

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