Core 4 - Parametric Equations

Question 1

What does a parametric equation do differently than a Cartesian equation?

Answer 1

It expresses the variables x and y in terms of a third parameter, usually t. This makes it easy to apply transformations.

Question 2

How do you find the co-ordinates when a parametric equation intercepts the axes?

Answer 2

Set the variables x and y =0. x=0 = y co-ordinate of interception, y=0 = x co-ordinate of interception.

Solve each equation, and write as two co-ordinates

Question 3

How do you convert parametric to cartesian equations?

Answer 3

Solve one equation for t, substitute into the other.

Question 4

What must you remember if one variable is defined in terms of t^2 when finding the cartesian?

Answer 4

Do not touch it!!

Use the other variable to solve for t, then substitute in, because the square root will give positive and negative answers and be a general mess

Question 5

What happens when you differentiate a constant e.g. E^-1

Answer 5

Differentiates to zero

Question 6

How do you find a cartesian equation if parameters involve sin(x) and cos(x)?

Answer 6

Rearrange x and y so they = sin(x) or cos(x), then square them and add them together, using identity sin^2(x) + cos^2(x)=1. Rearrange for required form.

Question 7

Having found the normal to a parametric curve, how do you whether the normal intercepts the curve again?

Answer 7

Substitute x and y parameters in terms of t into the equation of the normal, and solve the resulting equation.