Hello candidate,

Because of a restriction or limitation on the number of answering available on this platform, it's very difficult for me to derive you the exact equation for a common tangent to more than one parabola.

But here are the steps which you need to follow to derive the equation, first of all take the the common equation of a line which is y equal to MX + c and put the value in the equation of the parabola which is y square equal to 4ax and y square equal to 4bx. From these two equations we shall get two coordinates and using these two coordinates we can derive the equation of line.

Hope you found it helpful. If you have any further queries feel free to post it here!!