question_answer

   The length of a tangent at any point on the curve y = f(x) is intercepted between the point and the x-axis is of length 1. Find the equation of the curve.

A)  \[\log \left| \frac{1-\sqrt{1-{{y}^{2}}}}{y} \right|+\sqrt{1-{{y}^{2}}}=\pm \,\,x+c\]

B)  \[\log \left| \frac{1-\sqrt{1-{{y}^{2}}}}{y} \right|+\sqrt{1+{{y}^{2}}}=\pm \,\,2x+c\]

C)  \[\log \left| \frac{1+\sqrt{1+{{y}^{2}}}}{2y} \right|+\sqrt{\frac{1+{{y}^{2}}}{2}}=2x+c\]

D)  \[\log \left| \frac{2-\sqrt{2-{{y}^{2}}}}{y} \right|-\sqrt{1-{{y}^{2}}}=x+c\]

E)  None of these