Find the lines through the point (0,2) making angles `pi/3` and`(2pi)/3` with the x-axis. Also, find the lines parallel to the cutting the y-axis at a distance of 2 units below the origin.

Explanation

Equation of the line passing through `(x_1, y_1)` and making angle `theta` with the `x`-axis is, `=tan theta(x-x_1)`

For the first line: `(x_1, y_1)=(0,2), theta=fracpi3`

`(y-y_1)=tan theta(x-x_1)`

`(y-2)=(tan (2frac)pi3)(x-0) `

`y-2=sqrt3 x`

`sqrt3 x-y+2=0`

For the second line: `(x_1, y_1)`=`(O, 2)`,

`frac=theta2 pi3 `

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