Eliminate the parameter for the following parametric equations:
x(t)=t-2
y(t)=t^2-4
A) y=x^2+2x+8
B) y=x^2+4x+4
C) y=x^2+4x
D) y=x^2+4x+8
To eliminate the parameter, we need to express one variable in terms of the other variable. In this case, we need to express y in terms of x.
Given the parametric equations:
x(t) = t - 2
y(t) = t^2 - 4
To eliminate the parameter, we need to solve the first equation (x(t) = t - 2) for t in terms of x:
t = x + 2
Now substitute this value of t into the second equation (y(t) = t^2 - 4):
y = (x + 2)^2 - 4
y = (x^2 + 4x + 4) - 4
y = x^2 + 4x + 4 - 4
y = x^2 + 4x
Therefore, the equation that results from eliminating the parameter is y = x^2 + 4x.
Among the given options, the correct answer is C) y = x^2 + 4x.
I did the last one
You try this one.
t = x+2
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