TS EAMCET · Maths · Pair of Lines
If \(\operatorname{Tan}^{-1}(2 \sqrt{10})\) is the angle between the lines \(a x^2+4 x y-2 y^2=0\) and \(a \in Z\), then the product of the slopes of given lines is
- A \(\frac{3}{2}\)
- B \(\frac{2}{3}\)
- C \(-\frac{2}{3}\)
- D \(-\frac{3}{2}\)
Answer & Solution
Correct Answer
(D) \(-\frac{3}{2}\)
Step-by-step Solution
Detailed explanation
\( Ax^2+2Hxy+By^2=0 \implies A=a, H=2, B=-2 \) \( \tan\theta = \left| \frac{2\sqrt{H^2-AB}}{A+B} \right| \implies 2\sqrt{10} = \left| \frac{2\sqrt{2^2-a(-2)}}{a-2} \right| \) \( \sqrt{10} = \left| \frac{\sqrt{4+2a}}{a-2} \right| \implies 10 = \frac{4+2a}{(a-2)^2} \)…
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