AP EAMCET · Maths · Pair of Lines
PQR is a right angled isosceles triangle with right angle at \(\mathrm{P}(2,1)\). If the equation of the line \(Q R\) is \(2 x+y=3\), then the equation representing the pair of lines \(P Q\) and \(P R\) is
- A \(3 x^2-3 y^2-8 x y-10 x-15 y-20=0\)
- B \(3 x^2-3 y^2+8 x y+20 x+10 y+25=0\)
- C \(3 x^2-3 y^2+8 x y-20 x-10 y+25=0\)
- D \(3 x^2-3 y^2+8 x y+10 x+15 y+20=0\)
Answer & Solution
Correct Answer
(C) \(3 x^2-3 y^2+8 x y-20 x-10 y+25=0\)
Step-by-step Solution
Detailed explanation
\(m_{QR} = -2\) \(\tan 45^\circ = \left| \frac{m - m_{QR}}{1 + m m_{QR}} \right| \implies 1 = \left| \frac{m + 2}{1 - 2m} \right|\) \(\frac{m+2}{1-2m} = 1 \implies m+2 = 1-2m \implies 3m = -1 \implies m_1 = -1/3\) \(\frac{m+2}{1-2m} = -1 \implies m+2 = -1+2m \implies m_2 = 3\)…
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