Question

A curve C has the property that if the tangent drawn at any point P on C meets the co-ordinate axes at A and B, then P is the mid-point of AB. The curve passes through the point (1, 1). Determine the equation of the curve. 

Answer 1

The equation of the tangent at any point P(x, y) is

dy/y = – dx/x

∫dy/y = - ∫dx/x

log |y| = log c – log |x|

xy = c

which is passing through (1, 1), so c = 1 

Hence, the equation of the curve is

xy = 1