Indicate what type of conic section is represented by the eq

Indicate what type of conic section is represented by the equation. (Parabola, circle, ellipse, or hyperbola) x^2 - 16y^2 + 224x - 6y + 768 = 0

can you show the work

Solution

a=1, b=0, c=-16 comparing with the equation Ax² + Bxy + Cy² + Dx + Ey + F = 0

B² - 4AC = 0 - (4 x 1 x -16) = 64 >0

which implies it is a

Hyperbola: B² - 4AC > 0.