Given that x=3sinθ-2 and y=3cosθ+4.Show that (x+2)²+ (y-4)²=9

First, plug-in x and y as 3sinθ-2 and 3cosθ+4 into the equation, respectively:

Then, +2 and -2 cancel out and +4 and -4 cancel out as well, leaving you with:

We can factor out 3^2 = 9 from both equations:

We know from a trigonometric identity that , meaning we can reduce the equation to:

And therefore, we have shown that (x+2)^2 + (y-4)^2 = 9, if x=3sinθ-2 and y=3cosθ+4.

Hope this helped you.