The plots:-implicitplot command computes the two-dimensional plot of an implicitly defined curve.

The invalid input: invalid range for first variable error occurs when an unknown range is passed to the implicitplot command.

Example 1

The value of $a$ is undefined.

Solution:

The solution is to define $a$.

Example 2

In this instance, the first range is dependent on the second variable.  It is permissible to plot an implicit plot for which the second range depends on the first variable, but the first range must evaluate to numeric values.

Solution:

Specify a first range that is independent of the second variable.  For instance,