Equation of the hyperbola whose foci are (5,0) and (-3,0), eccentricity = 2, is

Concept:

The standard equation of a hyperbola:

where 2a and 2b are the length of the transverse axis and conjugate axis respectively and centre (h, k)

Note: The centre is the midpoint of the 2 foci.

The eccentricity = 

Length of latus recta = 

Distance from center to focus = 

Calculation:

Given foci are (5,0) and (-3,0)

Center =  = (1, 0)

Now distance of focus from the center = 

⇒ 

⇒ a² + b² = 16               ...(i)

The eccentricity = 

⇒ 2 =  

⇒ a = 2

Putting it in (i)

⇒ 4 + b² = 16

⇒ b² = 12

a² = 4

The equation of the hyperbola

⇒ 

⇒