Answer:
[tex]\frac{x^2}{61}-\frac{y^2}{37} =1[/tex]
Step-by-step explanation:
The standard equation of a hyperbola is given by:
[tex]\frac{(x-h)^2}{a^2} -\frac{(y-k)^2}{b^2} =1[/tex]
where (h, k) is the center, the vertex is at (h ± a, k), the foci is at (h ± c, k) and c² = a² + b²
Since the hyperbola is centered at the origin, hence (h, k) = (0, 0)
The vertices is (h ± a, k) = (±√61, 0). Therefore a = √61
The foci is (h ± c, k) = (±√98, 0). Therefore c = √98
Hence:
c² = a² + b²
(√98)² = (√61)² + b²
98 = 61 + b²
b² = 37
b = √37
Hence the equation of the hyperbola is:
[tex]\frac{x^2}{61}-\frac{y^2}{37} =1[/tex]
