let P(x;y) be point on curve                      S(4;0)

there fore according problem  PS  = 20 units

 

PS² = 400

(x-4)² + y² =400 

 

x² + y² + 16 - 8x = 400  

 

as 8x = y² + 16 

 

tht implies  y² +16 - 8x = 0

 

 therefore  x² = 400

 

                  x = 20 or - 20

 

put these x values in curve equation we get  y values as 12 or -12

 

therefore points are (20;12) and (20;-12)