Question

Sub 23
ques: 5

Find an equation of the hyperbola described:

Foci (0, -8) and (0, 8); difference of focal radii 10

Answer 1

As we see from the focuses situation, the main axis for hyperbola is an OY axis

Knowing, that the difference between the focal radii of hyperbola equals $2a$, we can calculate it:

$$2a = 10, \quad a = 5$$

Now, as we know

$$c^2 = a^2 + b^2, \quad \text{or} \quad 64 = 25 + b^2$$ $$b^2 = 39$$

Now, keeping in mind, that main axis is OY, we can write down the equation:

$$\frac{y^2}{25} - \frac{x^2}{39} = 1$$