:9x^2+16y^2+36x-32y-92=0 and find the vertices, focus, major axis and minor axis.

9x^2+36x+16y^2-32y=92.

(3x)^2+2*3x*6+6^2+(4y)^2-2*4y*4+4^2=92+6^2+4^2.

(3x+6)^2+(4y+4)^2 =144.

9(x+2)^2+16(y+1)^2=144.

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

a^2=16 a=+4, b=+3.

centre(h,k) : (-2,-1).

Vertictes (h+a,k),(h-a,k),

Verticies(2,-1),(-6,-1).

Co verticies (h,k+b),(h,k-b) :(-2,2),(-2,-4).

eccentricity e=sqrt(a^2-b^2)/a =sqrt(7)/4. =2.65/4.

foci (h+ae,0),(h-ae,k) (-2+2.65,0), (-2-2.65,0).

:(0.65,0),(-4.65,0).

length of major axis =2a=2*4=8.

length of minor axis =2b=2*3=6.