Answer:
Seee answer below.
Step-by-step explanation:
a. k = −1
If K=-1 the equation gets this form:
(x^2/-1) -y^2=1
There aren't natural numbers that being negative, adding them, we get 1 as result. So there is no graph for this equation.
b. k = 1
(x^2/1) -y^2=1
This is the natural form of the equation of an hyperbola. Attached you can find the graph.
c. k = 2
(x^2/2) -y^2=1
This is the natural form of the equation of an hyperbola. Attached you can find the graph.
d. k = 4
(x^2/4) -y^2=1
This is the natural form of the equation of an hyperbola. Attached you can find the graph.
e. k = 10
(x^2/10) -y^2=1
This is the natural form of the equation of an hyperbola. Attached you can find the graph.
f. k = 25
(x^2/25) -y^2=1
This is the natural form of the equation of an hyperbola. Attached you can find the graph.
g. Describe what happens to the graph of
x2 / k − y2 = 1 as k → [infinity].
As K is increasing the value of X will be tending to 0. So the equation for this will be:
− y^2 = 1.The solution for this is in the domain of the imaginary numbers.
