AP EAMCET · Maths · Pair of Lines
The square of the differences of the slopes of the lines represented by the equation
\[
x^2\left(\sec ^2 \theta-\sin ^2 \theta\right)-2 x y \tan \theta+y^2 \sin ^2 \theta=0 \text { is }
\]
- A 1
- B 2
- C 4
- D 8
Answer & Solution
Correct Answer
(C) 4
Step-by-step Solution
Detailed explanation
\(a = \sec ^2 \\theta-\\sin ^2 \\theta, 2h = -2 \\tan \\theta, b = \\sin ^2 \\theta\) \((m_1 - m_2)^2 = \frac{4(h^2 - ab)}{b^2}\) \((m_1 - m_2)^2 = \frac{4\left((-\\tan \\theta)^2 - (\sec ^2 \\theta-\\sin ^2 \\theta)(\\sin ^2 \\theta)\right)}{(\\sin ^2 \\theta)^2}\)…
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