Question

Find the equation of a line passing through (1, 2) and making angle of 30⁰ with y-axis.

Answer 1

Answer :

We know " The slope of the line is the tangent of the angle made by the line with positive direction of X – axis measured in the anticlockwise direction.

SO ,

Here that angle = 90$°$ - 30$°$ = 60$°$

As we know this line going to cut x and y axis at some point than that line and x and y axis form a right angle triangle ( as we know intersection point of two axis form a 90$°$ angle .
So,

Slope of equation m = tan 60$°$ = $\sqrt{3}$ ( As we know tan 60$°$ = $\sqrt{3}$ )

And we know equation of line when a point is given , where line is passing ,

( y - y ₁ ) = m ( x - x ₁ )

So ,

Our equation of line = ( y - 2 ) = $\sqrt{3}$ ( x - 1 )

y = $\sqrt{3}$ x - $\sqrt{3}$ + 2 ( Ans )