 Hello friends and how are you all doing today? That is discuss the question it says find the points on the curve x square plus y square minus 2x minus 3 equal to 0 at which the tangents are parallel to the x axis. So we are given x square plus y square minus 2x minus 3 equal to 0. Now I am differentiating the above equation with respect to x we get 2x plus 2y dy by dx minus 2 equal to 0. This implies 2y dy by dx is equal to 2 minus 2x. This implies y dy by dx is equal to 1 minus x or we have dy by dx equal to 1 minus x upon y. Here we took 2 common or we divided both the sides by 2 to get this. Now this is slope of the tangent x and y. Now the tangent is parallel to x axis. This is given to us in the question. This means that the slope of the tangent is equal to 0. This implies 1 minus x upon y is equal to 0. This implies 1 minus x is equal to 0 gives us the value of x as 1. So we have when the value of x is equal to 1 we have 1 square plus y square minus 2 into 1 minus 3 equal to 0 that is 1 plus y square minus 5 equal to 0 which gives us y square is equal to 4 or we have the value of y as plus minus 2. So the answer to the session is 1 comma plus minus 2 is or are the points on the curve x square plus y square minus 2x minus 3 is equal to 0 add to which the tangents are parallel to x axis. This completes the session. Hope you understood it well. Do take care of your calculations and have a nice day.