10.6 Plane Curves and Parametric Equations. Let x = f(t) and y = g(t), where f and g are two functions whose common domain is some interval I. The collection.

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10.6 Plane Curves and Parametric Equations

Let x = f(t) and y = g(t), where f and g are two functions whose common domain is some interval I. The collection of points defined by (x, y) = (f(t), g(t)) is called a plane curve. The equations x = f(t) y = g(t) where t is in I, are called parametric equations of the curve. The variable t is called a parameter.

Discuss the curve given by the parametric equations

Parabola with vertex at (0, 2) that opens to the right. Find the rectangular equation of the curve whose parametric equations are

Adam Johnson throws a tennis ball with an initial speed of 40 meters per second at an angle of 45 degrees to the horizontal. The ball leaves Adam Johnson’s hand at a height of 2 meters. (a) Find parametric equations that describe the position of the ball as a function of time.

(b) How long was the ball in the air? When the ball hits the ground y(t)=0. Solve as quadratic equation.

The ball was in the air for about 5.8 seconds. Not possible.

(c) When was the ball at its maximum height? (d) What was the maximum height of the ball? When y(t) has its maximum. The maximum height is meters at t=2.89 seconds.

(e) Use a graphing utility to simulate the motion of the baseball by simultaneously graphing the equations found in (a).

Find the parametric equations for the equation Let y = t.