Algebraically determine if the equation x^2+4y^2= 16

Question

is symmetric with respect to the x-axis, the y-axis, or the origin.? 

Answer 1

Step 1:

The equation is .

(i)

Test for Symmetry about the -axis:

Replace  with and simplify the equation.

If the resulting equation is equal to the original equation then it is symmetry about -axis.

The equation is symmetric with respect to -axis.

Step 2:

(ii)

Test for Symmetry about the -axis:

Replace with and simplify the equation.

If the resulting equation is equal to the original equation then it is symmetry about -axis.

The equation is symmetric with respect to -axis.

Step 3:

(iii)

Test for Symmetry about the origin:

Replace with , with as and simplify the equation.

If the resulting equation is equal to the original equation then it is symmetry about origin.

The equation is symmetric with respect to origin.

Solution:

The equation is is symmetric with respect to -axis, -axis and origin.