Select the correct answer. Which hyperbola has the smallest distance between the vertex and the focus belonging to the same branch?

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c

is it like a multiple choice? if so then i need the multiple choice so i can get and understanding on what the answers is so that i can explain it to you