First slide

Equation of line in Straight lines

Question

A Straight line passes through (4, 5) and makes an angle $60^{0}$ with x-axis in the positive direction. Its equation in the parametric form

Easy

A

x = $\sqrt{3} λ$ + 4, y = $λ$ + 5
B

x = $λ$ + 4, y = $\sqrt{3} λ$ + 5
C

x = $\sqrt{3} λ$ – 4, y = $λ$ + 5
D

x = $λ$ – 4, y = $λ$ + 5

Solution

$P (x_{1}, y_{1}) = (4, 5) θ = 60^{0}$
$x = x_{1} + r \cos θ, y = y_{1} + r \sin θ$
$\Rightarrow x = 4 + r . \frac{1}{2} = 4 + λ$
$\Rightarrow y = 5 + r . \frac{\sqrt{3}}{2} = 5 + \sqrt{3} λ$
Where $λ = \frac{r}{2}$

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