The rectangular equation that represents the parametric equation [tex]x=t^{\frac{1}{2} }[/tex] and y = 4t is:
[tex]y=4x^2[/tex] for [tex]x\geq0[/tex]
Note the given representations:
[tex]x=t^{\frac{1}{2} }[/tex]
[tex]y=4t[/tex]
Make t the subject of the formula from the expression [tex]x=t^{\frac{1}{2} }[/tex]
[tex]x^2=t^{\frac{1}{2}\times2\\\\x^2=t\\t=x^2[/tex]
Substitute [tex]t=x^2[/tex] into y = 4t
[tex]y=4x^2[/tex]
Therefore, the rectangular equation that represents the parametric equation [tex]x=t^{\frac{1}{2} }[/tex] and y = 4t is:
[tex]y=4x^2[/tex] for [tex]x\geq0[/tex]
Learn more on parametric equation here: https://brainly.com/question/14746714
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