MHT CET · Maths · Pair of Lines
The equation \(x^2-3 x y+2 y^2+3 x-5 y+2=0\) represents a pair of straight lines. If \(\theta\) is the angle between them, then the value of \(\cos \theta\) is equal to
- A \(\frac{1}{3 \sqrt{2}}\)
- B \(\frac{3}{\sqrt{10}}\)
- C \(\frac{2}{\sqrt{10}}\)
- D \(\frac{1}{5 \sqrt{2}}\)
Answer & Solution
Correct Answer
(B) \(\frac{3}{\sqrt{10}}\)
Step-by-step Solution
Detailed explanation
\(a=1, h=-\frac{3}{2}, b=2\) \(\tan \theta = \left| \frac{2\sqrt{h^2 - ab}}{a+b} \right| = \left| \frac{2\sqrt{(-\frac{3}{2})^2 - (1)(2)}}{1+2} \right|\)
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