Respuesta :
Given :
Two equations :
y = t³
x = t + 5
To Find :
Rectangular equation formed by eliminating the parameter.
Solution :
Putting value of t from second equation to first equation.
We get :
[tex]y = ( x-5)^3[/tex]
Also, t from equation first :
[tex]t = \sqrt[3]{y}[/tex]
Putting the value of t and equation two, we get :
[tex]x = \sqrt[3]{y}+5[/tex]
Therefore, rectangular equation is formed by eliminating the parameter is :
y = ( x - 5)³ and x = ∛y + 5 .
The rectangular equation is y = (x - 5)³ which is obtained from the parametric equations y = t³ and x = t + 5 option (3) y = (x - 5)³ is correct.
What are parametric equations?
A parametric equation in mathematics specifies a set of numbers as functions of one or more independent variables known as parameters.
The options are:
- y = (x + 5)³
- x = (y + 5)³
- y = (x - 5)³
- y = (x - 5)²
- It is given that:
The parametric equations are:
y = t³
x = t + 5
From the second equation that is x = t + 5
Take the value of t and plug in the equation y = t³:
t = x - 5
y = (x - 5)³
The above equation represents a cubic equation.
Thus, the rectangular equation is y = (x - 5)³ which is obtained from the parametric equations y = t³ and x = t + 5 option (3) y = (x - 5)³ is correct.
Learn more about the parametric function here:
brainly.com/question/10271163
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