Question

$4y^2-9x^2=36$ Find the points where it touches the axis

Answer 1

$4y^2-9x^2=36$

It touches $x-axis$ When $y=0$

$⟹-9x^2=36x^2=\frac{36}{-9}{x}^2=-4x=2i$

So the curve does not touch $x-axis$

It touches $y-axis$ When $x=0$

$⟹4y^2=36y^2=\frac{36}{4}{y}^2=9y=\pm 3$

So the curve touches $y-axis$ at $(\pm 3,0)$