Question

Find the equation of the curve in which the perpendicular from the origin upon the tangent is equal to the abscissa of the point of contact. 

Answer 1

The equation of the tangent to the curve at (x, y) is 

Y – y = (dy/dx)(X – x)

It is given that 

Integrating, we get

log |v² + 1| = log c – log |x|

(v² + 1) = c/x

x² + y² = cx

which is the required solution.