Question

The equations of the asymptotes of the hyperbola $2x^2+5xy+2y^2-11x-7y-4=0$ are

• A. $2x^2+5xy+2y^2-11x-7y-5=0$
• B. $2x^2+4xy+2y^2-7x11y+5=0$
• C. $2x^2+5xy+2y^2-11x-7y+5=0$
• D. none of the above

Answer 1

Answer: (A)

$2x^2+5xy+2y^2-11x-7y-5=0$

The pair of asymptotes and second degree curve differ by a constant
$\therefore$ Pair of asymptotes
$2x^2+5xy+2y^2-11x-7y+\lambda =0$..................(i)
Hence, Eq. (i) represents a pair of straight lines.
$\therefore \Delta =0\text{Then},2\times 2\times \lambda +2\times -\frac{7}{2}\times -\frac{11}{2}\times \frac{5}{2}-2\times {(-\frac{7}{2})}^2-2\times {(-\frac{11}{2})}^2-\lambda {\left(\frac{5}{2}\right)}^2=0\therefore \lambda =5$
From Eq. (i),
$\therefore$ Pair of asymptotes is $2x^2+5xy+2y^2-11x-7y+5=0$