Question

For the given​ equation, list the intercepts and test for symmetry.4 x squared plus y squared equals 4What are the​ intercept(s)? Select the correct choice below and fill in any answer boxes within your choice.

A.The​ intercept(s) is/are nothing.​(Type an ordered pair. Use a comma to separate answers as​ needed.)
B.There are no intercepts

Answer 1

x-intercepts: (1,0), (-1,0)

y-intercept: (0,2), (0,-2)

Explanation:

We are given the following in the equation:

`4x^2+y^2 = 4`

x-intercept:

It is the value of x for which y is zero.

`4x^2 + (0)^2 = 4\\4x^2 = 4\\x^2 = 1\\x = \pm 1`

x-intercepts: (1,0), (-1,0)

y-intercept:

It is the value of y for which x i 0.

`4(0)^2 + y^2 = 4\\y^2 = 4\\y = \pm 2`

y-intercept: (0,2), (0,-2)

Symmetry around y-axis:

`4(-x)^2 + y^2 =4 \\4x^2 + y^2 = 4`

Thus, it is symmetric around y-axis.

Symmetry around x-axis:

`4x^2 + (-y)^2 = 4\\4x^2 + y^2 = 4`

Thus, it is symmetric around x-axis.

Symmetry around origin:

`4(-x)^2 + (-y)^2 = 4\\4x^2 + y^2 = 4`

Thus, it is symmetric around origin.