TS EAMCET · Maths · Pair of Lines
The equation \(x^2-5 x y+p y^2+3 x-8 y+2=0\) represents a pair of straight lines. If \(\theta\) is the angle between them, then \(\sin \theta\) is equal to
- A \(\frac{1}{\sqrt{50}}\)
- B \(\frac{1}{7}\)
- C \(\frac{1}{5}\)
- D \(\frac{1}{\sqrt{10}}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{\sqrt{50}}\)
Step-by-step Solution
Detailed explanation
Comparing the given equation \[ x^2-5 x y+p y^2+3 x-8 y+2=0 \] with \(a x^2+2 h x y+b y^2+2 g x+2 f y+c=0\) we get \[ a=1, h=\frac{-5}{2}, b=p, g=\frac{3}{2}, f=-4 \text { and } c=2 \] Eq. (i) represents a pair of straight lines, if…
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