The center of a hyperbola is (−4,3) , and one vertex is (−4,7) . the slope of one of the asymptotes is 2.

what is the equation of the hyperbola in standard form?

The answer to your question is below

Step-by-step explanation:

C (-4, 3)

V (-4, 7)

asymptotes = 2 =

- This is a vertical hyperbola, the equation is

slope = 2

a is the distance from the center to the vertex = 4

b = 2(4) = 8

Step-by-step explanation:

The hyperbola centered at (h,k) has the following expression:

Where and are the length of the horizontal and vertical semi-axes, respectively.

Since the center and one vertex share the same vertical component (), it is easy to conclude that hyperbola has a vertical configuration (). The distance between the center and the known vertex is equal to the length of the vertical semi-axis. Therefore:

The slope of the hyperbola is given by the following relationship:

The length of the horizontal semi-axis is:

The standard form of the equation of the hyperbola is:

c.

step-by-step explanation:

she should of added 9^2 and 12^2. that is because it is a^2+b^2=c^2. c^2 is the hypotenuse and should always be bigger than the other two numbers. which is why she should of added 9 squared and 12 squared together instead of 15 squared.

just sum

10 + 10 = 20