 Hello and welcome to the session. Let us understand the following question today. If x and y are connected parametrically by the equations given below, without eliminating the parameter find d y by dx, we have x is equal to a sec theta and y is equal to b tan theta. Now let us write the solution given to us as x is equal to a sec theta and y is equal to b tan theta. Now dx by d theta is equal to a sec theta tan theta and dy by d theta is equal to b sec squared theta. So by chain rule, we have dy by dx is equal to dy by d theta multiplied by d theta by dx which is equal to dy by d theta is equal to b sec squared theta multiplied by d theta by dx is equal to the reciprocal of dx by d theta that is 1 by sec theta tan theta. Now we see here one sec theta gets cancelled by one sec theta so we are left with b by a sec theta by tan theta which is equal to b by a sec theta can be written as 1 by cos theta and tan theta can be written as sin theta by cos theta. So we see here cos theta and cos theta gets cancelled. So we are left with b by a 1 by sin theta which is equal to b by a cos sec theta which is our dy by dx hence the required answer is b by a cos sec theta. I hope you have answered the question. Bye and have a nice day.