Question:
Why do they call a rectangular hyperbola, rectangular and where the normal hyperbola looks like a rectangle and the rectangular hyperbola looks like a sqaure?

Hi Aarti,

The "rectangular" here refers to the right (= rect) angle between the asymptotes. (In the quadrangle that we call a rectangle, the word refers to the angles between adjacent sides; perhaps it should be called a "tetrarectangle.")

Cheers,
Chris