How to check for collisions?

Questions
1

So, say you had just a circle on screen and you you wanted it to print “touching” when you touch it. What are good methods to do this?

2

Here’s something I wrote a long time ago.

function setup()
    parameter.integer("a",1,400,200)    -- size of a axis
    parameter.integer("b",1,400,100)    -- size of b axis
    xc=250    -- center of ellipse x axis
    yc=400    -- center of ellipse y axis
end

function draw()
    background(40, 40, 50)    
    fill(255)
    ellipse(xc,yc,a*2,b*2)    -- draw ellipse   
    x=CurrentTouch.x    -- touched x value
    y=CurrentTouch.y    -- touched y value        
    fill(255,0,0)
    ellipse(x,y,5)  -- draw point  
    -- check if point is inside of ellipse or circle
    if (x-xc)^2/a^2+(y-yc)^2/b^2 <= 1 then 
        text("point in ellipse",xc,yc)        
    end    
end
3

Thanks!