The foci of a hyperbola are `(-5,12)` and `(10,20)` and it touches the `y`-axis . The length of its transverse axis, is

Options

A. `100`
B. `sqrt(89)//2`
C. `sqrt(89)`
D. `sqrt(50)`

Explanation

To solve the problem, we will follow these steps:

### Step 1: Find the distance between the foci
The foci of the hyperbola are given as \( F_1(-5, 12) \) and \( F_2(10, 20) \). We can use the distance formula to find the distance between these two points.

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
...