Parametric Curves?

Question

If the parametric curve starts at (5,-6) when t=0 and ends at (1,1) at t=1, then find a,b,c,d if the parametric equations are x=a+bt and y=c+dt!

Answer 1

(5,-6) at t=0 where x=a+bt and y=c+dt implies

x = 5 = a+bt = a+b*0 = a so a=5
y = -6 = c+dt = c+d*0 = c so c=-6

(1,1) at t=1 implies

x = 1 = 5 + bt = 5+b*1 = 5+b so 5+b=1 and b=-4
y = 1 = -6 + dt = -6+d*1 = -6+d so d-6=1 and d=7

So the curves are

x=5-4t
y=7t-6

Answer 2

0, 5=a 1, 1=5+bt or b=-4
0, -6=c 1, 1=-6+d or d=7
a=5, b=-4, c=-6, d=7 What you do is just plug into the equations with the numbers you know and find the answers. Soving by the substitution method. You can also solve this by determiniants

Answer 3

you have two eq for a and b and two eq for c and d

Solve when t = 0, 5=a + 0b and when t =1 1 = a + b
so a = 5, b = -4

and when t = 0 -6 = c + 0d and when t = 1 1 = c + d
so c = -6 and d = 7

Answer 4

hmm i like curves