Answer:
[tex]\frac{y^{2} }{81} -\frac{x^{2} }{40} }=1[/tex] is standard equation of hyperbola with vertices at (0, ±9) and foci at (0, ±11).
Step-by-step explanation:
We have given the vertices at (0, ±9) and foci at (0, ±11).
Let (0,±a) = (0,±9) and (0,±c) = (0,±11)
The standard equation of parabola is:
[tex]\frac{y^{2} }{a^{2} } -\frac{x^{2} }{b^{2} }=1[/tex]
From statement, a = 9
c² = a²+b²
(11)² = (9)²+b²
121-81 = b²
40 = b²
Putting the value of a² and b² in standard equation of parabola, we have
[tex]\frac{y^{2} }{81} -\frac{x^{2} }{40} }=1[/tex] which is the answer.
