Question

The portion of the tangent to xy $=a^2$ at any point on it between the axes is

• A. Trisected at that point
• B. bisected at that point
• C. constant
• D. with ratio $1:4$ at the point

Answer 1

Answer: (B)

bisected at that point

Let xy tangent at $(a,a)$
$x{y}^{\prime }+y=0$

$y^1=\frac{-y}{x}$

$y^{\prime }=-1$

$(y-a)=-1(x-a)$

Bisected by that point.

$y^{\prime }atB=\frac{-y}{x}$

$=\frac{-a{y}^2}{t{y}^2}$

$(y-\frac{a^2}{t})=\frac{-a^2}{t^2}(x-t)$

$x=0,y=\frac{2a^2}{t}$

$y=0,x=2t$

$(t,\frac{a^2}{t})$ to the mid point of (2+10) and $(0,\frac{2a^2}{t})$.
H.P.