question_answer

A curve passing through the point (1, 1) has the property that the perpendicular distance of the origin from the normal at any point P of the curve is equal to the distance of P from the x-axis. Determine the equation of the curve.

A)  \[{{x}^{2}}+{{y}^{2}}-6x=0,\]\[{{x}^{2}}-x+2=0\]

B)  \[{{x}^{2}}-{{y}^{2}}-3x=0,\]\[2x+2=0\]

C)  \[{{x}^{2}}+{{y}^{2}}-4x=0,\]\[x-4=0\]

D)  \[{{x}^{2}}+{{y}^{2}}+2x=0,\]\[x-1=0\]

E)  None of these