Question

The equation $16x^2+y^2+5xy-74x-75y+212=0$ represents

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

Answer 1

The correct option is C an ellipse

$△=abc+2fgh-a{f}^2-b{g}^2-c{h}^2$

$a=16,b=1,c=212,h=\frac{5}{2}$

$f=\frac{-75}{2},g=-37$

$△=16\times 1\times 212+2\times \frac{5}{2}\times \frac{75}{2}\times 37-16\times {\frac{75}{2}}^2$

$-1\times (-37{)}^2-212\times (\frac{5}{2}{)}^2$

$△=-14864.5\ne 0$

$h^2=\frac{25}{4}$

$ab=16$

$h^2<ab$ & $△\ne 0$

Hence it is equation of an ellipse.