Question

The equation 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. $2x^2$ + 5xy + $2y^2$ – 11x – 7y + 5 = 0
• C. $2x^2$ + 5xy + $2y^2$ – 11x – 7y + 7 = 0
• D. $2x^2$ + 5xy + $2y^2$ – 11x – 7y – 7 = 0

Answer 1

The correct option is B $2x^2$ + 5xy + $2y^2$ – 11x – 7y + 5 = 0

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