Answer:
(x+1)^2 / 9 - (y-2)^2 / 16 = 1
Step-by-step explanation:
B. on edge
The equation of the hyperbola is (x+1)^2/9 - (y-2)^2/16 = 1.
It is a curve in two-dimensional geometry having two parts they both are symmetric. In other words, It can be defined as the number of points in the two-dimensional geometry that have a constant difference from that point to two fixed points in the plane.
We have one focus of the hyperbola is located at (-6, 2)
One vertex of the hyperbola is located at (-4, 2)
The center of the hyperbola is at (-1, 2)
We know the standard form of a hyperbola is:
[tex]\rm \frac{(x-h)^2}{a^2} -\frac{(y-k)^2}{b^2}= 1[/tex]
Where (h, k) is the center of the hyperbola, the vertex of the hyperbola is (h[tex]\pm[/tex]a, k), and the focus is (h[tex]\pm[/tex]c, k).
Where [tex]\rm c^2=a^2+b^2[/tex]
Here h = -1, and k = 2
Vertex (-4,2), h - a = -4⇒ -1 -a = -4 ⇒ a = 3
Focus (-6, 2), h-c = -6 ⇒ -1 -c = -6 ⇒ c = 5
For b:
[tex]\rm 5^2=3^2+b^2[/tex]
[tex]\rm 25= 9 +b^2[/tex]
b = 4
Therefore the equation of the hyperbola is:
[tex]\rm \frac{(x+1)^2}{3^2} -\frac{(y-2)^2}{4^2}= 1[/tex] or
[tex]\rm \frac{(x+1)^2}{9} -\frac{(y-2)^2}{16}= 1[/tex]
Thus, the equation of the hyperbola is (x+1)^2/9 - (y-2)^2/16 = 1.
Learn more about the hyperbola here:
https://brainly.com/question/12919612
