It's not linear, it's quadratic. A linear relationship would be of the form y = mx +c
it is a linear model - both linear models and non linear models can be used to fit curves
in this case there is a constant and two parameters multiplying the predictor variables, that one of the predictor variables is simply the square of the other doesn't matter, the model is still linear in the parameters and still takes the standard form:

resulting plot looks like this:

so the OP has a bit of a problem if he's trying to predict values for the independent variable using the dependent variable