Question

The conic represented by the equation $x^2+y^2-2xy+20x+10=0$ is

• A. a parabola
• B. an ellipse
• C. a hyperbola
• D. a pair fo straight line

Answer 1

The correct option is A a parabola

On compairing the given eqaution with the equation
$a{x}^2+b{y}^2+2hxy+2gx+2fy+c=0$ we get
$a=b=1,h=-1,c=10,g=10$ and $f=0$
$\therefore \Delta =abc+2fgh-a{f}^2-b{g}^2-c{h}^2=10-100-10=-100\ne 0$
and $h^2=1=ab$
Hence given equation represents a parabola