Parametric Equations of x^2-y^2=1

In summary, the given equation x^2-y^2=1 represents a hyperbola. The concept of hyperbolas may be new to the person asking the question. The parametric equations for a curve cannot be determined as there are multiple possible equations for a single curve. The person responding suggests using hyperbolic sine and cosine, which have the property cosh2x-sinh2x=1.
  • #1
lemurs
30
0
given x^2-y^2=1 find the parametric equation...

i have no clue where to start... it looks like a cirlce equation but i know that not right so what the hell?
 
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  • #2
What you have there is the equation for a hyperbola, I'm guesing you haven't met hyperbolas before?
 
  • #3
Do you know what hyperbolic sine and cosine are?
 
  • #4
One point: there is no such thing as the parametric equations for a curve. A single curve can have expression in many different parametric equations. As Office Shreder said, do you know hyperbolic sine and cosine? They have the nice property that cosh2x- sinh2x= 1
 

Related to Parametric Equations of x^2-y^2=1

What are parametric equations?

Parametric equations are a mathematical representation of a curve or surface in terms of one or more independent parameters. These equations allow us to express the coordinates of points on the curve or surface in terms of the parameters.

How do you convert a Cartesian equation to parametric equations?

To convert a Cartesian equation, such as x^2-y^2=1, to parametric equations, we can let x=cos(t) and y=sin(t), where t is the parameter. This will result in the parametric equations x=cos(t) and y=sin(t).

What is the significance of the parameter in parametric equations?

The parameter in parametric equations represents a specific point on the curve or surface. By varying the parameter, we can generate different points on the curve or surface, allowing us to graph and analyze it in a more efficient manner.

How do you graph parametric equations?

To graph parametric equations, first choose a range of values for the parameter. Then, plug in these values to the parametric equations to get corresponding x and y coordinates. Plot these points on a graph and connect them to form the curve or surface represented by the equations.

What is the relationship between parametric equations and polar coordinates?

Parametric equations and polar coordinates are both ways to represent points on a curve or surface. While parametric equations use a parameter to describe the points, polar coordinates use an angle and a distance from the origin. Both systems can be converted to each other, making them interchangeable in some cases.

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