Question 970906
x^2-4y^2-6x-16y+29=0

rewrite
x^2-6x  -4y^2-16y  = -29

rewrite
x^2-6x - 4(y^2+4y) = -29

complete the square

x^2-6x+9- 4 (y^2+4y+4) =  -29   + 9 (from x) -16 (from y) = -36

(x-3)^2 - 4(y+2)^2 =-36
Divide by 36

[(x-3)^2/36} - [(y+2)^2]/9 = -1

This is a hyperbola.