Given equation is 16x² + y² + 8xy - 74x - 78y + 212 = 0

We know that for ax² + 2hxy + by² + 2gx + 2fy + c = 0 is a parabola if h² = ab and abc + 2fgh - af² - bg² - ch²≠0

Here a = 16, b = 1, h = 4, g = - 37, f = - 39, c = 212.

⇒ abc + 2fgh - af² - bg² - ch² = (16)(1)(212) + (2)(- 39)(- 37)(4) - (16)(- 39)² - (1)(- 37)² - (212)(4)²

⇒ abc + 2fgh - af² - bg² - ch² = 3392 + 11544 - 24336 - 1369 - 3392

⇒ abc + 2fgh - af² - bg² - ch² = - 14161

⇒ h² = (4)²

⇒ h² = 16

⇒ h² = (16)(1)

⇒ h² = ab

The given curve is parabola.

∴The correct option is B