If lines represented by equation $\mathrm{px}^2-\mathrm{qy}^2=0$ are distinct, then

If lines represented by equation $\mathrm{px}^2-\mathrm{qy}^2=0$ are distinct, then
  1. $\mathrm{p} \mathrm{q} < 0$
  2. $\mathrm{p}+\mathrm{q}=0$
  3. $\mathrm{p} \mathrm{q}>0$
  4. $\mathrm{pq}=0$

Solution

Lines represented by $\mathrm{px}^2-\mathrm{qy}^2=0$ are distinct. Here $\mathrm{h}=0, \mathrm{a}=\mathrm{p}$ and $\mathrm{b}=-\mathrm{q}$ Now $\mathrm{h}^2-\mathrm{ab}>0 \Rightarrow 0+\mathrm{pq}>0 \Rightarrow \mathrm{pq}>0$

Asked in: MHT CET 2021 (22 Sep Shift 2)

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