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AP EAMCET · Maths · Straight Lines

Assertion (A): The difference of the slopes of the lines represented by
\(\mathrm{y}^2-2 \mathrm{xysec}^2 \alpha+\left(3+\tan ^2 \alpha\right)\left(-1+\tan ^2 \alpha\right) \mathrm{x}^2=0 \text { is } 4\)
Reason (R): The difference of the slopes represented by
\(a x^2+2 h x y+b y^2=0 \text { is } \frac{2 \sqrt{h^2-a b}}{|b|}\)

  1. A Both \(\mathrm{A}\) and \(\mathrm{R}\) are true and \(\mathrm{R}\) is the correct explanation of \(\mathrm{A}\)
  2. B Both \(\mathrm{A}\) and \(\mathrm{R}\) are true but \(\mathrm{R}\) is not correct explanation of \(A\)
  3. C A is true but \(R\) is false
  4. D \(A\) is false but \(R\) is true
Verified Solution

Answer & Solution

Correct Answer

(A) Both \(\mathrm{A}\) and \(\mathrm{R}\) are true and \(\mathrm{R}\) is the correct explanation of \(\mathrm{A}\)

Step-by-step Solution

Detailed explanation

Since the difference of the slopes of the lines \(a x^2+2 h x y+b y^2=0\) is given by \(\frac{2 \sqrt{h^2-a b}}{|b|}\) Now the given line is \(y^2-2 x y \sec ^2 \alpha+\left(3+\tan ^2 \alpha\right)\left(-1+\tan ^2 \alpha\right) x^2=0\) So the difference of slope is…