Answer:
 (b) hyperbola
Step-by-step explanation:
The x- and y-terms are both squared. When written in standard form, they have opposite signs. That means the equation describes a hyperbola.
 x^2 -14x +4 = 9y^2 -36y . . . . . given
 x^2 -14x +4 -9y^2 +36y = 0 . . . . subtract right side
 x^2 -14x +49 -9(y^2 -4y +4) = 45 -36 . . . . complete the squares
 (x -7)^2 -9(y -2)^2 = 9 . . . . . . write as squares
 (x -7)^2/9 -(y -2)^2 = 1 . . . . . . standard form equation for hyperbola
