Find an equation for the hyperbola described Graph the equat

Find an equation for the hyperbola described. Graph the equation. Center at (-5,-1); focus at (-5, - 8); vertex at (-5, - 7) Write an equation for the hyperbola. - = 1 (Type exact answers for each term, using fractions as needed.) Select the graph which correctly describes the hyperbola.

Solution

Vertex , centre and focus all lie on vertical line x= -5

so, y^2 part must be added to the equation:

vertex is 6 units from centre ,so a=6

focus if 7 units from centre so, c=7 ; b^2 = c^2 -a^2 = 7^2 -6^2 = 49-36 =13

So, (y+1)^2/36 - (x+5)^2/13 =1