 Hello and welcome to the session. In this session we discuss the following question that says, find the points on the curve y equal to xq at which the slope of the tangent is equal to the y-coordinate of the point. Let's now proceed with the solution. The given curve is y equal to xq, let this be equation one. We have to find the points on this curve at which the slope of the tangent is equal to the y-coordinate of the point. For this we suppose that the required point be x1, y1, that is x-coordinate is x1 and y-coordinate is y1. Now the point x1, y1 lies on the curve given by equation one. Therefore, this means we have y1 is equal to x1q, let this be equation two. Next differentiating equation one with respect to x we get dy by dx is equal to 3x square. Now dx at the point x1, y1 is equal to 3x1 square. Now this dy by dx at the point x1, y1 is the slope of the tangent at the point x1, y1. The question is given that the slope of the tangent at that point on the curve is equal to the y-coordinate of the point. So according to the question x1 square would be equal to the y-coordinate of the point which is y1, three equation three. Now from equation two we have y1 equal to x1q. So on the equations two and three that is these three equations we have square is equal to x1q which means x1q minus 3x1 square is equal to zero or you can say x1 square into x1 minus 3 the whole is equal to zero which means that either x1 square equal to zero or x1 minus 3 is equal to zero. That is we have x1 equal to zero or x1 equal to three. So we now get two values for x1 either zero or three put in x1 equal to zero in equation two we have y1 equal to zero therefore we say for x1 equal to zero we get y1 equal to zero. Next put in x1 equal to three in equation two we get y1 equal to that is twenty seven therefore we say for x1 equal to three we get y1 equal to twenty seven. Hence we have three twenty seven the required points zero zero and three twenty seven. So this is our final answer and the study solution of this question.