Y^2=6/x what kind of equation is this?

Question

this is for our assignment in calculus related to hyperbola

Answer 1

y²=6/x is the same as x=6/y², which can be written f(y)=6/y². Therefore f(x)=6/x², whose parent is p(x)=1/x², known as the reciprocal squared function. It could also be considered to belong to the exponential function family, because 1/x²=x^-2 may be considered to belong to exp(x)=xⁿ.

Effectively, graphically y²=6/x is x²=6/y (y=f(x)=6/x²) rotated clockwise 90° so that (x,y) becomes (y,-x). For example, the point (1,6) on x²=6/y becomes (6,-1) on y²=6/x; and (-1,6) on x²=6/y becomes (6,1) on y²=6/x; and vice versa.