10 SolutionThe center and vertices of the given hyperbola li

Solution

The center and vertices of the given hyperbola lie on the horizontal line y =-5. The center is (1,-5) and the vertices are (-1,-5) and (3,-5).Further, the branches of the hyperbola are side by side, so that its equation is of the form (x-1)²/a² –(y+5)²/b² = 1 . Further, the vertex is 2 units from the center so that a = 2. The asymptotes pass through the points (1,-5), (2,-3) and (1,-5),(0,-3) respectively so that the slope s of the asymptotes are ± 2 , hence b/a = 2 so that b = 2a = 4. Hence, the equation of the given hyperbola is (x-1)²/4 – (y+5)²/16 = 1