Question

Equation $3x^2+7xy+2y^2+5x+3y+2=0$ represents

• A. pair of straight lines
• B. ellipse
• C. hyperbola
• D. None of the above

Answer 1

Answer: (D)

None of the above

Given equation of pair of lines is
$3x^2+7xy+2y^2+5x+3y+2=0$
Here $a=3,h=\frac{7}{2},b=2,g=\frac{5}{2},f=\frac{3}{2},c=2$
Now, $abc+2fgh-a{f}^2-b{g}^2-c{h}^2$
$=3\left(2\right)\left(2\right)+2\left(\frac{3}{2}\right)\left(\frac{5}{2}\right)\left(\frac{7}{2}\right)-3{\left(\frac{3}{2}\right)}^2-2{\left(\frac{5}{2}\right)}^2-2{\left(\frac{7}{2}\right)}^2$
$=-\frac{22}{4}$
$\therefore$ It does not represent a pair of straight lines. Here coefficient of $xy$ is not zero, it does not represent an ellipse and hyperbola