Option : (B)
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.
