Question

The equation 16x² + y² + 8xy − 74x − 78y + 212 = 0 represents 

Options

• a circle 

• a parabola 

•  an ellipse 

•  a hyperbola 

Answer 1

a parabola
Comparing the given equation with ax² + by² + 2hxy + 2gx+2fy + c =0, we get: 

\[a = 16, b = 1, h = 4\] 

We have: 

\[h^2 = 16 = ab\] 

Thus, the given equation represents a parabola.