 Hi and welcome to the session. Let us discuss the following question. Question says, find the equation of a curve passing through the point 0-2 given that at any point x, y on the curve, the product of the slope of its tangent and y-coordinate of the point is equal to the x-coordinate of the point. First of all, let us understand that slope of the tangent to a curve at point x, y is equal to dy upon dx. This is the key idea to solve the given question. Let us now start with the solution. Now we are given in the question that the product of the slope of the tangent at xy or we can say at point xy, y-coordinate is equal to the x-coordinate of the point. Now we know slope of the tangent at point xy is equal to dy upon dx and y-coordinate of this point is y. So here we can write ydy upon dx is equal to x, we know x-coordinate of this point is equal to x. Now separating the variables in this equation we get ydy is equal to xdx. Now integrating both the sides of this equation we get integral of ydy is equal to integral of xdx. Now using this formula of integration we can find both of these integrals. Now we get integral ydy is equal to y square upon 2 and integral of xdx is equal to x square upon 2 plus c, where c is the constant of integration. Let us name this equation as equation 1. Now we are given that the curve passes through the point 0 minus 2. So we will substitute 0 for x and minus 2 for y in this equation. Now we get square of minus 2 upon 2 is equal to 0 square upon 2 plus c. Now simplifying further we get 2 is equal to 0 plus c. Now this further implies 2 is equal to c or we can simply write c is equal to 2. Now substituting c is equal to 2 in equation 1 we get y square upon 2 is equal to x square upon 2 plus 2. Multiplying both the sides of this equation by 2 we get y square is equal to x square plus 4. Subtracting x square from both the sides of this equation we get y square minus x square is equal to 4. This is the required equation of the curve. So this is our required answer. This completes the session. Hope you understood the solution. Take care and keep smiling.