TS EAMCET · Maths · Straight Lines
Assertion (A) The lines \(2 x^2+5 x y+2 y^2=0\) and \(x-2 y+1=0\) form a right angled triangle. Reason (R) The equation \(a x^2+2 h x y+b y^2=0\) represents a pair of perpendicular lines if \(a+b=0\) Then choose the correct answer
- A \((A)\) is false, (R) is true
- B \((\mathrm{A})\) is true, \((\mathrm{R})\) is false
- C (A) is true, ( \(\mathrm{A})\) is true, but \(\mathrm{R}\) is not the correct explanation to (A)
- D (A) is true, \((\mathrm{R})\) is true and \((\mathrm{R})\) is the correct explanation to (A)
Answer & Solution
Correct Answer
(C) (A) is true, ( \(\mathrm{A})\) is true, but \(\mathrm{R}\) is not the correct explanation to (A)
Step-by-step Solution
Detailed explanation
Given, equation of lines \(2 x^2+5 x y+2 y^2=0\) \(\begin{array}{rlrl}\Rightarrow & 2 x^2+4 x y+x y+2 y^2 & =0 \\ \Rightarrow & 2 x(x+2 y)+y(x+2 y) & =0 \\ \Rightarrow & & (x+2 y)(2 x+y)=0 \\ \Rightarrow & (2 x+y) & =0 \\ \text { and } & & (x+2 y) & =0\end{array}\) Now, slope of…
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