B. 233/100
C. 2100/33
D. 233/100
Answer:
Step-by-step explanation:
It is not B.233. 100 MY GIVEN ME BAD...
The standard form equation for this hyperbola, when vertices are (+-5,0) and one focus is (6,0), is x²/25 - y²/11 = 1.
In the question, we are given a hyperbola with vertices at (+-5,0) and one focus at (6,0). A hyperbola is defined by its distances from a given point to the two different foci, and its standard form equation along the x-axis can be written as
(x-h)²/a² - (y-k)²/b² = 1
, where (h, k) is the center of the hyperbola, a represents the distance from the center to each vertex, and b represents the distance from the center to each co-vertex. In this case,
h = 0
, since the center of the hyperbola is at the origin. The value of
a = 5
is the distance from the center to each vertex. Finally, the square of the distance c from the center to each focus is defined as
c² = a² + b²
, so we can find
b = sqrt(c² - a²)
. Here, c = 6, so b = sqrt(6² - 5²) = sqrt(11). Thus, the standard form equation of this hyperbola is
x²/25 - y²/11 = 1
.
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