Question

For each value of kk specified in parts (a)–(e), plot the set of points in the plane that satisfy the equation
x2 / k − y2 = 1.
a. k = −1
b. k = 1
c. k = 2
d. k = 4
e. k = 10
f. k = 25
g. Describe what happens to the graph of
x2 / k − y2 = 1 as k → [infinity].

Answer 1

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.