Question

The equation $13x^2-18xy+37y^2+2x+14y-2=0$ represents

• A. a pair of straight lines
• B. a circle
• C. an ellipse
• D. a hyperbola

Answer 1

The correct option is C an ellipse

$13x^2-18xy+37y^2+2x+14y-2=0$
On comparing with $a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0,$ we have
$a=13,h=-9,b=37,g=1,f=7,c=-2$
Then $△=abc+2fgh-a{f}^2-b{g}^2-c{h}^2$
$=\left(13\right)\left(37\right)(-2)+2\left(7\right)\left(1\right)(-9)-13(7{)}^2-37(1{)}^2+2(-9{)}^2$
$=-1600\ne 0\cdots \left(i\right)$

Now, $h^2-ab=81-481<0\cdots \left(ii\right)$
From $\left(i\right)$ and $\left(ii\right)$,
the above equation represents an ellipse.