The equation `16 x^2+y^2+8x y-74 x-78 y+212=0` represents a. a circle b. a parabola c. an ellipse d. a hyperbola

Options

A. a circle
B. a parabola
C. an ellipse
D. a hyperbola

Answer

B

Explanation

Comparing the given equation with `ax^(2)+2hxy+by^(2)+2gx+2gy+c=0` we get
`a=16, b=1, c=212, h=4, g=-37" and " f=-39`
`:." "abc+2fgh-af^(2)-bg^(2)-ch^(2)`
`=3392+11544-24336-1369-3392ne0`
and, `h^(2)-ab=16-16=0`
Hence, the given equation represets a parabola.