The equation of the hyperbola is (( x +2 )² / 16 ) - (( y -1)²/9) = 1.
What is a Hyperbola?
A hyperbola is a plane curve that is generated when a point moves such that its difference of the distance from two fixed points is constant.
The standard equation of Hyperbola is
((x-h)²/a²) - ((y-k)²/b²) = 1
Here (h,k) is the center of the hyperbola.
The vertex is (h±a, k)
The focus is (h±c, k)
c² = a² + b²
One focus of a hyperbola is located at (-7, 1).
One vertex of the hyperbola is located at (-6, 1)
The center is (-2, 1).
Comparing with the standard equations,
h = -2 , k = 1
h±a = -7
-2 + a = -6
a = -4
h±c = -7
-2 + c = -7
c = -5
By the formula
c² = a² + b²
25 = 16 +b²
b = 3
The equation of the hyperbola is
(( x +2 )² / 16 ) - (( y -1)²/9) = 1
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