Question

Find the equation, Centre, vertices, co-vertices, foci, equations of assymptotes and eccentricity of the hyperbola traced by the points that moves so that the differences of its distance from (-4,4) and (-4,6) is 6.

Answer 1

google is your friend. Try this to get going:

https://people.richland.edu/james/lecture/m116/conics/hypdef.html

Answer 2

I think the question have mistake.
I tried my best but the graph is not like hyperbola.
The value of a is greater than c therefore, b is undefined

Answer 3

I agree. Since the distance between the foci is only 2, there is no way that the condition can be met.