The required equation of the hyperbola is expressed as
[tex]\frac{x^2}{10}- \frac{y^2}{15}=1 \\[/tex]
The standard form for calculating the equation of a parabola along the x-axis is expressed as:
[tex]\frac{(x-k)^2}{a^2}-\frac{(y-h)^2}{b^2} = 1 \ ............. 1[/tex] where:
(h, k) is the center
(k±c, h) are the foci
[tex]x=h\pm\frac{a^2}{c}[/tex] is the directrix
From the question given, we can see that foci = (±5, 0)
k±c, h = ±5, 0
k = 0
h = 0
c = 5
From the directrix,
[tex]x=h\pm\frac{a^2}{c}\\x =0\pm\frac{a^2}{5}\\\pm2 = \pm\frac{a^2}{5}\\a^2 = 10\\[/tex]
Also, we need to know that;
a²+b² = c²
10 + b² = 5²
b² = 25 - 10
b² = 15
Substituting the gotten values into the equation of a hyperbola;
[tex]\frac{(x-0)^2}{10}- \frac{(y-0)^2}{15} =1\\\frac{x^2}{10}- \frac{y^2}{15} =1\\[/tex]
This gives the required equation of the hyperbola
Learn more on the equation of hyperbola here: https://brainly.com/question/20409089
