Write an equation for the hyperbola with vertices (0, - 1) and (0, 3) and foci (0, - 3) and (0, 5) .

Please see the explanation for the process. The equation is

y²/3²−x²/4²=1

Explanation:

There are two types of hyperbolas, one where a line drawn through its vertices and foci is horizontal, and one where a line drawn through its vertices and foci is vertical. This hyperbola is the type where a line drawn through its vertices and foci is vertical. We know this by observing that it is the y coordinate that changes when we move from a focus point to a vertex.

The general equation for this type of hyperbola is:

(y−k)²a²−(x−h)²b²=1

Observe that the x coordinate of the foci and the vertices is 0; this tells us that  

h=0(y−k)²a²−(x−0)²b²=1

The value of k is the sum of y coordinate of the vertices divided by two:

k=−3+32=0(y−0)²a²−(x−0)²b²=1

Please notice that when  

x=0,y=±3

; this allows us to find the value of "a":

(3−0)²a²−(0−0)²b²=1(3−0)²a²=1(3−0)²=(a²)a=3(y−0)²3²−(x−0)²b²=1

Let c = the distance between the the center point and focus = 5. The equation for the square of this distance helps us to find the value of b:

c²=a²+b²5²=3²+b²b²=25−9b²=16b=4(y−0)²3²−(x−0)²4²=1

Simplifying a bit:

y²3²−x²4²=1

Step-by-step explanation:

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a

step-by-step explanation:

a

step-by-step explanation:

there is a formula i can give you:

it is r^2*n*sin(360/n) divided by 2 where r represents the "radius" and n is the number of sides.

plug them in:

(10sqrt(3))^2*6*sin(360/6) divided by 2

100*3*6*sin(60) divided by 2

900*sin(60)

900*sqrt(3)/2

450*sqrt(3)

approx is 779.4 cm^2