Let P(x, y) be a point on the curve y = f(x). Then slope of the normal to the curve is \(-\frac{1}{(\frac{dy}{dx})}\)
∴ equation of the normal is
Since, this normal passes through (2,0), we get
Integrating both sides, we get
This is the general equation of the curve. Since, the required curve passed through the point (2, 3), we get
22 + 32 = 4(2) + c
∴ c = 5
∴ equation of the required curve is x2 + y2
= 4x + 5.