Final answer:
To solve for the hyperbola equation, we use the formula (x - h)^2/a^2 - (y - k)^2/b^2 = 1. We find the center of the hyperbola using the given vertices and the distance from the center to focus. Using these values, we substitute them into the equation to get the hyperbola equation.
Step-by-step explanation:
To solve for the hyperbola equation, we need to use the formula: (x - h)^2/a^2 - (y - k)^2/b^2 = 1. Using the given information, we can determine the values of h, k, a, and b. Let's start by finding the center of the hyperbola using the given vertices:
Center (h, k) = ((x1 + x2)/2, (y1 + y2)/2) = ((-4 + -4)/2, (2√35 + -2√25)/2) = (-4, 0)
The distance from the center to focus is given as square root of 230, which is equal to c, the distance from the center to the focus. We can use this information to find the values of a and b:
c^2 = a^2 + b^2
a^2 = c^2 - b^2 = 230 - b^2
Since c^2 = a^2 + b^2, we can substitute the values of h, k, a, and b into the equation:
(x + 4)^2/a^2 - y^2/b^2 = 1