Answer:
The equation of the hyperbola [tex]\frac{x^2}{25} - \frac{y^2}{3696} = 1[/tex]
Step-by-step explanation:
Given hyperbola vertices are (5,0) and (-5,0)
The foci of the hyperbola is (61,0) and (- 61,0) so the foci is lie on x-axis
here the vertex a =5 and foci ('c')= 61
we know the condition [tex]c^{2} = a^2+b^2[/tex]
now substitute a =5 and c= 61
b^2 = 61^2 - 5^2 = 3696
a^2 = 25
The equation of the hyperbola [tex]\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1[/tex]
The equation of the hyperbola [tex]\frac{x^2}{25} - \frac{y^2}{3696} = 1[/tex]
