TS EAMCET · Maths · Parabola
If \(2 x+3 y+12=0\) and \(x-y+4 \lambda=0\) are conjugate with respect to the parabola \(y^2=8 x\), then \(\lambda\) is equal to
- A \(2\)
- B \(-2\)
- C \(3\)
- D \(-3\)
Answer & Solution
Correct Answer
(D) \(-3\)
Step-by-step Solution
Detailed explanation
Using the condition that if two lines \(l_1 x+m_1 y+n_1=0\) and \(l_2 x+m_2 y+n_2=0\) are conjugate w.r.t. parabola \(y^2=4 a x\), then \[ l_1 n_2+l_2 n_1=2 a m_1 m_2 \] Given conjugate lines are \(2 x+3 y+12=0\) and \(x-y+4 \lambda=0\) and equation of parabola is \(y^2=8 x\).…
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