Question

Find the equation of hyperbola whose foci are (4, 2) and (8, 2) and eccentricity is 2.
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Answer 1

Given :

foci : (4 , 2) and (8 , 2)

e = 2

To find :

Equation of hyperbola

Solution :

The center of the hyperbola is the midpoint of the line joining the two focii

So, the coordinates of the center are,

(4+8/2 , 2+2/2) i.e., (6,2)

a×e = 2

a × 2 = 2

a = 1

x² _ y² = 1

a²     b²

(x - 6)² _ (y - 2)²  = 1

   a²           b²

b² = a²(e² - 1)

b² = 1(2² - 1)

b² = 3

(x - 6)² _ (y - 2)²  = 1

   1            3

The equation of Hyperbola is (x - 6)² _ (y - 2)²  = 1

                                                       1              3