Parametric Equations for an Ellipse

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In summary, the given rectangular equation is ((y-2)^2)/49)-((x-1)^2)/9)=1. This equation is similar to x^2+y^2=1 and represents a geometric figure. A parametrization can be found by dividing the equation by cos2x.
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metking92
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Write a pair of parametric equations for the figure whose rectangular equation is
((y-2)^2)/49)-((x-1)^2)/9)=1


please help me
 
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  • #2
Compare it to the equation [itex]x^2+y^2=1[/itex] which is almost the same. Does this equation look familiar? Do you what kind of geometric figure it represents? Can you find a parametrization for this simplified problem?
 
  • #3
Hi i am sorry but i still don't understand this. Is there anyway you can make it simpler.
 
  • #4
metking92 said:
Hi i am sorry but i still don't understand this. Is there anyway you can make it simpler.

Here is a clue

if sin2x+cos22=1

and you divide throughout by cos2x, what do you get?
 

FAQ: Parametric Equations for an Ellipse

What is a parametric equation?

A parametric equation is a mathematical representation of a curve or surface that defines each point in terms of one or more independent variables, called parameters.

Why are parametric equations important?

Parametric equations are important because they allow us to describe complex shapes and curves in a more simplified and efficient way. They also allow for more flexibility in how we manipulate and analyze these shapes.

How do you write a parametric equation?

A parametric equation is typically written in the form of x = f(t) and y = g(t), where x and y represent the coordinates of a point on the curve and t is the parameter. The functions f(t) and g(t) represent the relationship between the parameter and the coordinates of the point.

What are the advantages of using parametric equations?

One advantage of using parametric equations is that they can describe curves and shapes that are not easily represented by traditional equations. They also allow for more precise and accurate calculations and can be used to solve complex problems in physics, engineering, and other fields.

Can parametric equations be used in real-world applications?

Yes, parametric equations are commonly used in real-world applications, such as computer graphics, robotics, and physics. They are also used in calculating the motion of objects in space and designing curved structures in architecture and engineering.

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