Given the parametric equations below, eliminate the parameter t to obtain an equation for y as a function of x {(x(t) = 7 sqrt(t)),(y(t) = 5 t + 2):}
y(x) =?
+130560 x(t) = 7√t → √t = x /7 → t = x^2 / 49
y(t) = 5t + 2 and substituting, we have
y(x) = (5/49)x^2 + 2 .
Notice that we must restrict the domain of this function to x ≥ 0....the reason for this is that x(t) in the original parametric equation isn't defined for t < 0
Here's a graph of both forms......https://www.desmos.com/calculator/abugghcton
+130560 x(t) = 7√t → √t = x /7 → t = x^2 / 49
y(t) = 5t + 2 and substituting, we have
y(x) = (5/49)x^2 + 2 .
Notice that we must restrict the domain of this function to x ≥ 0....the reason for this is that x(t) in the original parametric equation isn't defined for t < 0
Here's a graph of both forms......https://www.desmos.com/calculator/abugghcton
