Determine the line where C is by eliminating the parameter t ....so that you will be dealing with x and y only, as the coordinates are in x and y only.

y = 8 -t

So, t = 8 -y

Then,

x = 2 +2t

x = 2 +2(8 -y)

x = 2 +16 -2y

x = 18 -2y

2y = -x +18

y = (-1/2)x +9 ----------the line where C is.

If AB is the hypotenuse of the right triangle with C as the right angle, then, by Pythagorean theorem,

(AB)^2 = (AC)^2 +(BC)^2 ----------(i)

Let C be point C(x,y).

Umm, so it is simpler to express the x in terms of y.

Since x = 18 -2y, so,

C = C(18-2y,y)

Then in (i),

(9-2)^2 +(2-3)^2 = [((18-2y)-2)^2 +(y-3)^2] +[(18-2y)-9)^2 +(y-2)^2]

Expand, simplify and solve for y.

Then, x = 18 -2y.

You should get two possible C's......(6,6) and (8,5).