Please help me to understand transposing equations. In this example I need to find y

Question

x^2=y^2-r^2/y^2

Thank you for your help

Answer 1

I will assume you meant:
x^2 = (y^2 - r^2)/y^2 , (or else it becomes a real mess involving a quadratic equation in y^4)

Let me know otherwise

on my assumption,
x^2 y^2 = y^2 - r^2

y^2 - x^2 y^2 = r^2
y^2(1 - x^2) = r^2
y^2 = r^2/(1 - x^2)

y = ± r/(√(1-x^2) , where -1 < x < 1