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# Category Archives: Parametric Equations and Curves

## Parametric Equation problems

## Parametric Equation Sketch & *X*–*Y* Equation Conversion example question

Sketch the given Parametric Equation and find its corresponding *X*–*Y* Equation:

Solution to this **Parametric Equations & Curves **practice problem is given in the video below!

## Parametric Equation Sketch & *X*–*Y* Equation Conversion example problem

Sketch the given Parametric Equation and find its equivalent *X*–*Y* Equation:

Solution to this **Parametric Equations & Curves **practice problem is given in the video below!

## Parametric Equation Sketch & *X*–*Y* Equation Conversion example

Find Parametric Equations from the given *X*–*Y* equation:

Circle with radius 3, centered at (2, 1) and drawn counterclockwise.

Solution to this **Parametric Equations & Curves **practice problem is given in the video below!

## Parametric Equation Sketch & *X*–*Y* Equation Conversion example question

Derive Parametric Equations from the given *X*–*Y* equation:

Line from (-2, 4) to (6, 1).

Solution to this **Parametric Equations & Curves **practice problem is given in the video below!

## Parametric Equation Sketch & *X*–*Y* Equation Conversion example problem

Find Parametric Equations by using the given *X*–*Y* equation:

from (2, -2) to (0, 2).

Solution to this **Parametric Equations & Curves **practice problem is given in the video below!

## Parametric Equations: Points of Intersection of Two Curves example

Find the coordinates of the points of Intersection of two given Parametric Curves:

Solution to this **Parametric Equations & Curves **practice problem is given in the video below!

## Parametric Equations of a PROJECTILE example problem

A projectile is fired at an angle of inclination *α*, with 0 < *α *< π/2, at an initial speed of *v*_{o}. Parametric equations for its path can be shown to be ** x** =

*v*

_{o}

*t*cos(

*α*),

**=**

*y**v*

_{o}

*t*sin(

*α*) – (

*gt*²)/2, with

*t*representing time.

a) Eliminate the *t* parameter and find the value of *t* when the projectile hits the ground.

b) Sketch the path of the projectile for the case *α* = π/6, *v*_{o} = 32 ft/sec, *g* = 32 ft/sec ².

Solution to this **Parametric Equations of a Projectile **practice problem is given in the video below!

## Parametric Equations: Object Position, Velocity & Speed example question

Find the Position, Velocity and Speed of an Object by using the following Parametric Equation:

Solution to this **Parametric Equations & Curves **practice problem is given in the video below!

## Slope of the Parametric Curve example problem

Find the Slope of the Tangent Line to the Curve

Solution to this **Parametric Equations & Curves **practice problem is given in the video below!

## Parametric Curves: Coordinates of the Points of Vertical & Horizontal Tangent Lines example

Find the Coordinates of the Points of Vertical and Horizontal Tangent Lines to the Curve

Solution to this **Parametric Equations & Curves **practice problem is given in the video below!

## Parametric Curves: Arc Length example question

Find the Arc Length of a Parametric Curve

Solution to this **Parametric Equations & Curves **practice problem is given in the video below!

## Parametric Curves: Area example problem

Find the Area enclosed by a Parametric Curve

in the interval

Solution to this **Parametric Equations & Curves **practice problem is given in the video below!

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