(x+1)^2/9 -(y-3)^2/16 =1

Question

(x+1)² - (y-3)² =1 

   9.          16. 

 

Find the center , foci,vertices, and asymptotes of the hyperbola 

Answer 1

Center is (-1,3) as revealed in the (x-h)² and (y-k)² expressions.For this type of hyperbola, the transverse axis runs horizontally (through the center) since the y-related terms are subtracted from the x-related terms in this format.

 

a=3(square root of x-related denominator) and b = 4, and b² = c² - a².  This means that c = 5.

 

Foci are 5 units to the left and to the right of the center, therefore their coordinates are (-6,3) and (4,3).

 

In point-slope form, the equations of the asymptotes are y-3 = ±(4/3)(x+1).

 

I leave something for you to do: figure the coordinates of the two vertices.  Hint: easy if you make a sketch showing transversal running through the designated Center.