The required equation is \(x = \dfrac{4}{y-1} + 4\).
Hyperbola
It is the locus of a point such that the difference of the distance from P to two fixed-point remains constant.
Given
Asymptotes of the hyperbola are x=4 and y=1.
Find the equation of a hyperbola.
How to get the equation of hyperbola?
x=4 and y=1 can be written as
x-4=0 and y-1=0
Then the product of asymptote and constant is equal to zero.
That is
\((x-4)(y-1) + \lambda = 0\\\)
Let it passes through the origin (0,0) then
\(\begin{aligned} (0-4)(0-1)+ \lambda &= 0\\\lambda &= -4\\\end{aligned}\)
Then our equation become
\(\begin{aligned} (x-4)(y-1) - 4 &= 0\\x &= \dfrac{4}{y-1} + 4 \\\end{aligned}\)
Thus, the required equation is \(x = \dfrac{4}{y-1} + 4\).
More about the hyperbola link is given below.
https://brainly.com/question/12919612
