# How do you determine whether the graph of #y^2=(4x^2)/9-4# is symmetric with respect to the x axis, y axis, the line y=x or y=-x, or none of these?

##### 1 Answer

The graph is symmetrical, with respect to the axes. There is no symmetry, with respect to the bisectors

#### Explanation:

graph{x^2/8-y^2.4-1=0 [-10, 10, -5, 5]}

The equation is

Here,

So, if (x, y) is a point on the graph, then (x, -y), (-x, y) and (-x, -y) lie on

the graph. And so, the graph is symmetrical about both the axes.

origin, through

Referred to the new X and Y axes, the equation f(x, y) = 0

becomes

Now, only

symmetry about the ( same ) origin.

There is no symmetry about the new axes.

So, there is no symmetry about