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The distance of the variable point P which has coordinates x, y, z from the fixed points (0, 0, 1) and (0, 0, -1) are denoted by u and v respectively. New variable ξ, η, ϕ are defined by  and ϕ is the angle between the plane y = 0 and the plane containing the three points, i.e.  over 1 ≤ ξ < ∞, -1 ≤ η < 1, 0 ≤ ϕ < 2π. The Jacobian of  has the value , then 

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Concept:

 .............(i)

Calculation:

Given, 

 ...........(ii)

 ............(iii)

Solving (ii) and (iii), we get:

 and 

 .......(iv)

Putting values of equations (ii), (iii), and (iv), we get:

​​

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