Write parametric equations of the line passing through $(4, 5)$ having inclination $60 °$ .

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x = 4 - \frac{x}{2}, y = 5 - \frac{\sqrt{3}}{2} r

x = 2 + \frac{x}{2}, y = 5 + \frac{\sqrt{3}}{2} r

x = - 2 + r, y = 7 + \frac{\sqrt{3}}{2} r

x = 4 + \frac{r}{2}, y = 5 + \frac{\sqrt{3}}{2} r

answer is D.

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Detailed Solution

The parametric equations are

x = x_{1} + r \cos θ, y = y_{1} + r \sin θ

Where $(x_{1}, y_{1}) = (4, 5)$ and $θ = 60 °$

$x = 4 + r \cos 60 °, y = 5 + r \sin 60 °$

$x = 4 + r (\frac{1}{2}), y = 5 + r (\frac{\sqrt{3}}{2})$

$x = 4 + \frac{r}{2}, y = 5 + \frac{\sqrt{3}}{2} r$

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