Q. 145.0( 1 Vote )

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Answer :

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

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