how do you know that
(x-2x)/(x+1) is a hyperbola?
Thank you!
(x-2x)/(x+1)
=-x/(x+1)
= -1 + 1/(x+1)
substitute x'=x+1
= -1 + 1/x'
Hence a hyperbola shifted one unit downwards
... and one unit to the left
To determine the type and shape of a conic section, such as a hyperbola, we need to examine its equation. A general equation of a hyperbola can be given in the form:
((x-h)^2)/(a^2) - ((y-k)^2)/(b^2) = 1
where (h,k) represents the center of the hyperbola, and 'a' and 'b' correspond to the semi-major and semi-minor axes, respectively.
Now let's look at the equation you provided: (x - 2x)/(x + 1)
We can simplify this equation by combining like terms in the numerator:
-x / (x + 1)
We can see that this equation does not have the form of a general hyperbola equation. In a hyperbola equation, there should be both an 'x' term and a 'y' term, with coefficients and squared terms.
Therefore, based on the given expression, it is not appropriate to conclude that (x - 2x)/(x + 1) represents a hyperbola.