Save by clicking here (with the right mouse button) the file on your computer (change the name if you want, but leave ".htm").
At this point you can use it to calculate the distance for any parametric curve.
Just open the source code, edit x(t) and y(t), and run "save".  You can repeat this several times.
 

First example.

The distance from (10, 10) and the curve x=2+2*cos(t), y=−1+5*sin(t):

distance = 9.64470018696
nearest point of the curve = (2.815578657, 3.565380224) 		    

function x(t) { with(Math) {
return  2+2*cos(t)
}}
function y(t) { with(Math) {
return  -1+5*sin(t)
}}

We can draw the graph with JavaScript; for example, see the script curve_P  (see the code;  se also here).


 

Other x(t),  y(t)

The distance from (−1, 1) and the curve x=3·t/(1+t³), y=3·t²/(1+t³) (Folium of Descartes):

distance = 0.55934880423712
nearest point of the curve = (−1.33573753, 0.55261717) 		   

function x(t) { with(Math) {
return  3*t/(1+pow(t,3))
}}
function y(t) { with(Math) {
return  3*t*t/(1+pow(t,3))
}}
d = 0.5593488042371204  Q = (-1.3357375259792503,0.5526171679078099)
        t = -0.41371688461225     a = -0.4137169  b = -0.4137168
d = 0.5593488042371205  Q = (-1.3357375278902461,0.5526171693419127)
        t = -0.413716885094     a = -0.413717  b = -0.413716
d = 0.5593488042371205  Q = (-1.3357375309486323,0.5526171716370724)
        t = -0.413716885865     a = -0.41372  b = -0.41371
d = 0.5593488042371255  Q = (-1.335737587019048,0.5526172137150007)
        t = -0.4137169     a = -0.5  b = -0.4
d = 0.5593488044301476  Q = (-1.335749884071111,0.5526264420378972)
        t = -0.41371999999999786     a = -20  b = 20

A function

The distance from (2, −1) and the graph of x → x²:

distance = 1.949088133432
nearest point of the curve = (0.553573773, 0.306443922) 		        

function x(t) { with(Math) {
return  t
}}
function y(t) { with(Math) {
return  pow(t,2)
}}
d = 1.9490881334319283  Q = (0.55357377306562,0.3064439222261065)
        t = 0.55357377306562     a = 0.55357377  b = 0.55357378
d = 1.9490881334319283  Q = (0.55357377308585,0.30644392224850414)
        t = 0.55357377308585     a = 0.5535737  b = 0.5535738
d = 1.9490881334319283  Q = (0.55357377338,0.30644392257417163)
        t = 0.55357377338     a = 0.55357  b = 0.55358
d = 1.9490881334319287  Q = (0.5535738,0.30644395204644)
        t = 0.5535738     a = 0.5  b = 0.6
d = 1.949088133449685  Q = (0.5535700000000006,0.30643974490000064)
        t = 0.5535700000000006     a = -10  b = 10

Graphs like the ones shown here can be plotted also with R (see).