MHT CET · Maths · Pair of Lines
If lines represented by equation \(\mathrm{px}^2-\mathrm{qy}^2=0\) are distinct, then
- A \(\mathrm{p} \mathrm{q} < 0\)
- B \(\mathrm{p}+\mathrm{q}=0\)
- C \(\mathrm{p} \mathrm{q}>0\)
- D \(\mathrm{pq}=0\)
Answer & Solution
Correct Answer
(C) \(\mathrm{p} \mathrm{q}>0\)
Step-by-step Solution
Detailed explanation
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 \(\mathrm{h}^2-\mathrm{ab}>0 \Rightarrow 0+\mathrm{pq}>0 \Rightarrow \mathrm{pq}>0\)
Here \(\mathrm{h}=0, \mathrm{a}=\mathrm{p}\) and \(\mathrm{b}=-\mathrm{q}\)
Now \(\mathrm{h}^2-\mathrm{ab}>0 \Rightarrow 0+\mathrm{pq}>0 \Rightarrow \mathrm{pq}>0\)
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