Hello, Doubled144314!

I will limit my answers to Quadrant 1.

You can generalize the results if you like.

We note that

We have: .

Multiply by

. . . .

. . . .

. . . . . . . . . .

There are two cases: .

Case (1): .

Case (2): .

. . . . . . . .

. . . . . . . .

Therefore: .