AP EAMCET · Maths · Straight Lines
The equation of the line common to the pair of lines \(\left(\mathrm{p}^2-\mathrm{q}^2\right) \mathrm{x}^2+\left(\mathrm{q}^2-\mathrm{r}^2\right) \mathrm{xy}+\left(\mathrm{r}^2-\mathrm{p}^2\right) \mathrm{y}^2=0\) and \((l-\mathrm{m}) \mathrm{x}^2+\) \((\mathrm{m}-\mathrm{n}) \mathrm{xy}+(\mathrm{n}-l) \mathrm{y}^2=0\) is
- A \(x+y=0\)
- B \(x-y=0\)
- C \(x+y=p q r\)
- D \(x-y=p q r\)
Answer & Solution
Correct Answer
(B) \(x-y=0\)
Step-by-step Solution
Detailed explanation
We have given equations of lines are: \(\left(p^2-q^2\right) x^2+\left(q^2-r^2\right) x y+\left(r^2-p^2\right) y^2=0\) ...(i) And \((\ell-m) x^2+(m-n) x y+(n-\ell) y^2=0\) ...(ii) On comparing these two equations, we get \(p^2-q^2=\ell-m, q^2-r^2=m-n \& r^2-p^2=n-\ell\) Note…
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