Calculating trigonometric functions by not using a calculator??

My formulas are: y=(x+a)^2 x=(-y+a)^2 I would like to solve for a where they touch (exact solution). Here is a graph demonstrating what I mean: As you can see, I have attempted to solve for a by making them closer and closer. I think 1.100917368760402698 ≤ a ≤ 1.100917368760402699, but floating point error may have reduced the accuracy of that range, but it should be near those numbers at least. There will also be a negative solution of a , which will be exactly negative I believe.

Hello, I find it hard to understand the regions of integral when solving multivariable integrations, such as in double integration. I would like to discuss and learn about strategies and methods on how to go through the process of facilitating knowledge about the region/interval of the ​​integration. Would you like to share your thought process when you solving a double integral in polar coordinates? for example: Regards /Anhard