Q90 / 160 · AP EAMCET 2021 (20 Aug Shift 2) · Mathematics

If the lines represented by the equation $2 x^{2} - p x y + 2 y^{2} = 0$ are real then the value of ' $p$ ' lies in the interval

Solution

As we know, $a x^{2} + 2 h x y + b y^{2} = 0$ , represents a pair of straight lines when $h^{2} - a b \geq 0$

So, $2 x^{2} - p x y + 2 y^{2} = 0$

represent pair of straight lines iff

$\frac{p^{2}}{4} - 4 \geq 0$

$\Rightarrow (p - 4) (p + 4) \geq 0$

$p \in (- \infty, - 4) \cup (4, \infty)$

Hence, the correct answer is option: 'C'.