We can eliminate the parameter by isolating t in one of the equations and substituting into the other. From the equation for x(t), we have:
t = (x/2)^2
Substituting this into the equation for y(t), we get:
y = 4((x/2)^2)^2 + 3
Simplifying this expression, we have:
y = 2x^2 + 3
Therefore, the equation in terms of x and y is:
y = 2x^2 + 3.
2) Eliminate the parameter for the following parametric equation. Show all your work. Simplify as far as you can.
x(t)=2√t
y(t)=4t^2+3
3 answers
sorry.
4((x/2)^2)^2 + 3 = 4(x^2/4)^2 + 3 = 4(x^4/16) + 3 = x^4/4 + 3
4((x/2)^2)^2 + 3 = 4(x^2/4)^2 + 3 = 4(x^4/16) + 3 = x^4/4 + 3
You are correct! I apologize for my mistake in the previous response. The correct elimination of parameter is as follows:
From the equation for x(t), we have:
t = (x/2)^2
Substituting this into the equation for y(t), we get:
y = 4t^2 + 3 = 4(x/2)^4 + 3
Simplifying this expression, we have:
y = (x^4)/4 + 3
Therefore, the equation in terms of x and y is:
y = (x^4)/4 + 3.
From the equation for x(t), we have:
t = (x/2)^2
Substituting this into the equation for y(t), we get:
y = 4t^2 + 3 = 4(x/2)^4 + 3
Simplifying this expression, we have:
y = (x^4)/4 + 3
Therefore, the equation in terms of x and y is:
y = (x^4)/4 + 3.