simplify the given equation and graph xy-x+y=0
(it is on rotation of axes. please answer in order for me to have a guide in my studies tonight)
factor it
y(x+1) = x
y = x/(x+1)
a rotated hyperbola , with asymptote at x = -1
http://www.wolframalpha.com/input/?i=plot+y+%3D+x%2F(x%2B1)
Can you expalain a litte specific sir? I really cant get it T.T please.
cot2θ = 0 so θ=45°
Then just do the rotation matrix stuff to find the equation in the new coordinates.
Thanks Sir! :)
To simplify the given equation xy - x + y = 0, we can rearrange it to isolate the terms that contain x and y together:
xy - x + y = 0
Rearranging, we get:
xy + y = x
Now, let's isolate x:
xy + y = x
x = xy + y
Factoring out the common factor y on the right side, we get:
x = y(x + 1)
Now, let's graph the equation.
To graph the equation xy - x + y = 0, we can rewrite it in terms of y:
x(y + 1) = y
Now, we can divide both sides of the equation by (y + 1):
x = y / (y + 1)
To graph this equation, we can choose different values for y and calculate the corresponding values of x. Here are a few points to get started:
When y = -2:
x = (-2) / (-2 + 1) = -2
So, one point on the graph is (-2, -2).
When y = -1:
x = (-1) / (-1 + 1) = undefined
When y = 0:
x = 0 / (0 + 1) = 0
So, another point on the graph is (0, 0).
When y = 1:
x = 1 / (1 + 1) = 1/2
So, another point on the graph is (1/2, 1).
By calculating more points using different values of y, you can sketch the graph of the equation xy - x + y = 0.