Eliminate the parameter

Question

X=1/4t²  y=t

Answer 1

Alternatively, 

 

Sub in Y at the beginning

 

X=1/4t² Y=t

 

Becomes:

 

X=1/4Y²

 

Solve for Y:

 

Y²⁼4x

 

|Y|=√4x=2√x

 

(Note: |Y| is the absolute value of Y, a more correct alternative to the plus/minus symbol)

 

Answer 2

To eliminate the parameter T, from our equations we have to substitute one into the other.  The equation y = t allows us to substitute into x=1/4t².  We get the relation: x = 1/4y².  If you want it in function form, you'll end up with two equations, one positive and one negative due to the square root.

Answer 3

x = (1/4)t²

 

4x = t²

 

√4x = √t²

 

±2√x = t

 

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y = t

 

y = ±2√x