Find the location of the center vertices and foci for the hy

Find the location of the center, vertices, and foci for the hyperbola described by the equation. a) Center: (13,-4); Vertices: (3, -7) and (3,-11); Foci: (3,-4) and (3,-13) b) Center: (13, -4); Vertices: (3,-7) and (3,-1); Foci: (3,- 13) and (3,-4) c) Center: (3,-4); Vertices: (3, -7) and (3,-1); Foci: (13,-14) and (3,-14) b) Center: (13,-4); Vertices: (3, -7) and (3,-l) oci: (3,-4- 13) and (3,-4) e) none of these

Solution

( y + 4)^2 /9 - ( x- 3)^2 / 4 = 1

standrad equation of vertical hyperbola is

( y - k)^2 / a^2 - ( x - h)^2 / b^2 = 1

center = ( 3 , -4 )

vertices are given by ( h, k+a) , ( h , k - a )

hence, vertices are ( 3 , -1 ) ( 3, -7 )

foci is given by ( h , k+c) , ( h , k - c)

c = sqrt (a^2 - b^2 )

c = sqrt 13

hence, foci are ( 3 , - 4 + sqrt 13 ) , ( 3 , -4 - sqrt 13 )

option e is correct

siince foci doest match with any of the options