If a curve passes through the point (1,1) and at any point (x, y) on the curve, the product of the slope of its tangent and x coordinate of the point is equal to the y coordinate of the point, then the curve also passes through the point

Step-by-step solution

Let the equation of the curve by y=f(x) and curve passes through the point (1,1) , So, f(1)=1 Also, we know that at any point (x, y) on the curve, the product of the slope of its tangent and x co-ordinate of the point is equal to the y co-ordinate of the point. aligned y x & = d y d x x y^ & =y aligned y^ y = 1 x On integrating both sides w.r.t. x , we get aligned |y| & =| In | x +e^c y & =k x, where k=e^c aligned Now, we can use the fact that the curve passes through the point (1,1) to find the value of k . l =k(