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Parametric Coordinates

We can express the coordinate of a point of the hyperbola x2/a2 – y2/b2 = 1 in terms of a single parameter, say θ.
 
1431_Parametric Coordinates.JPG
 
In the adjacent figure OM = a sec θ and PM = b tan θ. Thus any point on the curve, in parametric form is x = a secq, y = b tanθ.
 

In other words, (a sec θ, b tan θ) is a point on the hyperbola for all values of θ. The point (a secθ, b tanθ) is briefly called the point ‘θ’.

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