The parametric equations for a curve in the x-y plane are x=2+t^2 and y=4-3t. Determine the points where the curve intersects the x-axis.
To determine the points where the curve intersects the x-axis, we need to find the values of t when y = 0.
Given the parametric equation:
x = 2 + t^2
y = 4 - 3t
We can set y = 0 and solve for t:
4 - 3t = 0
3t = 4
t = 4/3
Now let's substitute this value of t back into the equation for x:
x = 2 + (4/3)^2
x = 2 + 16/9
x = 18/9 + 16/9
x = 34/9
Therefore, when y = 0, the curve intersects the x-axis at the point (34/9, 0).