Question

Given the parametric equations x(t)=a+bt and y(t)=c+dt, if the parametric curve starts at (−1,−1) when t=0 and ends at (1,0) at t=1, what are the values of b, and c?

Answer 1

The values of b and c are 2 and 0, respectively.

Step-by-step explanation:

To find the values of b and c, we need to determine the equations for x(t) and y(t) using the given information. The parametric equations are x(t) = a + bt and y(t) = c + dt. Since the curve starts at (-1,-1) when t = 0, we substitute these values into the equations to get:

x(0) = a + b(0) = -1

y(0) = c + d(0) = -1

From the first equation, we know that a = -1. Plugging this value into the second equation, we have:

-1 + d(0) = -1

d(0) = 0

Since the curve ends at (1,0) when t = 1, we substitute these values into the equations to get:

x(1) = -1 + b(1) = 1

y(1) = c + d(1) = 0

From the first equation, we can solve for b:

b = (1 - (-1)) / 1 = 2

From the second equation, we know that c = 0. Therefore, the values of b = 2 and c = 0.