A curve is drawn such that the slope at any point P = (x,y) is equal to x. The curve represents a family of

It is given that the slope of the curve at any point P is equal to x.

It is also known that, to find the slope at any point P(x,y), we can find $$\ \frac{\ dy}{dx}$$ of the curve at that point P.

For $$\ \frac{\ dy}{dx}$$ of a curve to be equal to x, the original curve must be of the form $$\ ax^2\ +c$$, where a and c are any constants.

Now, y= $$\ ax^2\ +c$$ represents a family of parabolas.

Hence, option B