Question

y²- xy-6x² =0 find the acute angle between the pair of line represents by following equation​

Answer 1

There can be many ways, but as always, I'll go with the intuitive one.

Let's do some algebra,

x2−y2=0x2−y2=0

⟹x2=y2⟹x2=y2

⟹x=±⟹x=± yy

Or y=xy=x and y=−xy=−x are the two lines depicted by this conic.

We are familiar that they both are inclined at 45°45° with the axes, but on opposite sides, which also means that their slopes are equal but opposite in sign parity, which can be confirmed from the equations too.

Therefore, 45°+45°=90°45°+45°=90°

Or, because the product of the slopes is −1−1, therefore the lines are perpendicular to each other at the origin.