Question

Without graphing, determine whether each equation has a graph that is symmetric with

respect to the x-axis, the y-axis, the origin, or none of these.

(a) Y^2=-6/x^2

please show all steps

Answer 1

There is no solution to this equation, ie there are no points in 3 dimensional geometry that satisfy your given equation.

So no graph can be constructed from your equation, therefore your graph is not symmetric to any axis or origin.

Your equation can be written as

x^2y^2 = -6

Lhs  is always positive but rhs is negative.

Hence no solution