Answer:
The equation of hyperbola : [tex]\frac{y^{2} }{49 } - \frac{x^{2} }{32 }[/tex]
Step-by-step explanation:
Given - This hyperbola is centered at the origin.
Foci: (0,-9) and (0,9) Vertices: (0,-7) and (0,7)
To find - Find its equation.
Solution -
We know that,
Equation of Hyperbola is represented by
[tex]\frac{y^{2} }{a^{2} } - \frac{x^{2} }{b^{2} }[/tex]
Now,
Given that,
Foci : F(0, -9) and F'(0, 9)
So,
c = 9
And
Vertices : A(0,-7) and A'(0,7)
So,
a = 7
Also, we know that,
c² = a² + b²
⇒b² = c² - a²
⇒b² = 9² - 7²
⇒b² = 81 - 49
⇒b² = 32
So,
The equation of hyperbola becomes
[tex]\frac{y^{2} }{49 } - \frac{x^{2} }{32 }[/tex]
