Find the angle between the parabolas y2 = 4ax & x2= 4by at their point of intersection other than the origin ?

The given curves are y2 = 4ax  .......(1)

and x2 = 4by    .......(2)

Finding point of intersection of two curves:

Now, x = 0 ⇒ y = 0

∴ Points of intersection of (1) and (2) are (0, 0) and

On differentiating (1) and (2), we get

Angles between (1) and (2) at

Let θ be the acute angle between (1) and (2) at, then

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