Find the equation of the curve such that the portion of the x-axis cut off between the origin and the tangent art a point is twice the abscissa and which passes through the point (1,2).

Options

A. xy=1
B. xy=2
C. xy=3
D. xy=0

Answer

b

Explanation

Let P (x,y) be any point on the curve and PM the perpendicular to X-axis PT the tangent at P meeting the axis of x at T, s geiven OT= 2x , OM = x Equation of the tangent at P(x,y)is
` Y - y = (dy)/(dx) (X-x)`

It intersects the axis of X, where Y = 0
`rArr -y = (dy)/(dx) (X-x) rArr X = x - y (dx)/(dy) =OT`
Hence,` x - y (dy)/(dy) = 2x rArr (dx)/2 + (dy)/y =0`
This passes through (1,2)
` :. C = 2`
` :." The required curve is xy " = 2`