 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 multiplied by theta minus sin theta and y is equal to a multiplied by 1 plus cos theta. Now, let us write the solution. Given to us is x is equal to a multiplied by theta minus sin theta and y is equal to a multiplied by 1 plus cos theta. Now, dx by d theta is equal to a multiplied by 1 minus cos theta and dy by d theta is equal to a multiplied by minus sin theta. Now, by chain rule, 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 a multiplied by minus sin theta multiplied by d theta by dx which is equal to 1 by a multiplied by 1 minus cos theta. Now, we see here a and a gets cancelled, so we are left with minus sin theta divided by 1 minus cos theta. Now, minus sin theta can be written as minus 2 sin theta by 2 cos theta by 2 and 1 minus cos theta is equal to 2 sin square theta by 2. Now, we see that this 2 and 2 gets cancelled and 1 sin theta gets cancelled by 1 sin theta by 2. So, we are left with minus cos theta by 2 divided by sin theta by 2 which is equal to minus cos theta by 2 which is our dy by dx. Hence, the required answer is minus cot theta by 2. I hope you understood the question. Bye and have a nice day.