question_answer 53)

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 any y-coordinate of the point is equal to the x-coordinate of the point.  

Answer:

We know that slope of tangent to the curve y = f(x) at any point (x, y) is             Integrating both sides, we get             As it passes through (0, ?2), so put x = 0, y = ?2                                    which is the required equation of curve.