f(x)=a/x (x cannot be 0), and g(x)=ax+k. Where a and k are positive constants.?

Question

The line y=g(x) is a tangent to the curve y=|f(x)| at the point P, and cuts the curve y=|f(x)| at the point Q.

Show that k=2a.

Answer 1

|a/x| = ax+k
=> a/x = +/- (ax+k)
=> a = +/- (ax^2+kx)
=> a = - (ax^2+kx) OR => a = + (ax^2+kx)
=> ax^2+kx+a=0

tangent => 1 solution
=>b^2 = 4ac = 0
=> k^2 - 4*a*a = 0

the rest is easy

Answer 2

The Point P is at(-1,a), so:
a= a(-1) +k -> k = 2a

Answer 3

if:-a/x=ax+k

ax^2+k x+a=0

k^2-4a^2=0
k=2a