Question

The parametric equations x = t − 4 and y = t 2 5t represent a plane curve. which of the following rectangular equations represents the plane curve? y = x2 − 3x − 4 y = x2 5x y = x2 8x 21 y = x2 13x 36

Answer 1

The given parametric equations x = t - 4 and y = t^2/5t can be converted into the rectangular equation y = (1/5)x + 4/5.

Step-by-step explanation:

The given parametric equations are x = t - 4 and y = t^2/5t. To convert these parametric equations into rectangular form, we can solve the first equation for t and substitute it into the second equation.

From x = t - 4, we have t = x + 4.

Substituting t = x + 4 into y = t^2/5t, we get y = (x + 4)^2/(5(x + 4)).

Simplifying further, we have y = (x + 4)/(5) = (1/5)x + 4/5.

Therefore, the rectangular equation representing the plane curve is y = (1/5)x + 4/5.