Question

Eliminate the Parameter x=√t , y=4t+1

a) t = (x²)/4
b) t = (y-1)/4
c) t = x²
d) t = (y-1)²/16

Answer 1

To eliminate the parameter from the given parametric equations, solve for t in the equation x=√t and substitute it into y=4t+1, yielding y=4x²+1.

Step-by-step explanation:

To eliminate the parameter from the parametric equations x=\(\sqrt{t}\) and y=4t+1, you can solve one of the equations for t and then substitute that expression into the other equation. Since you have the equation x=\(\sqrt{t}\), you can square both sides to get t=x^2. Now, you can replace t in the equation y=4t+1 with x^2 to eliminate the parameter t. This gives you the equation y=4x^2+1, which is the Cartesian form of the equation. There are no elements from the original question related to the quadratic formula or its application.