AP EAMCET · Maths · Pair of Lines
The orthocentre of the triangle formed by the lines \(2 x^2-3 x y+y^2=0, x+y=1\) is
- A \(\left(\frac{1}{4}, \frac{1}{4}\right)\)
- B \(\left(\frac{1}{3}, \frac{1}{3}\right)\)
- C \(\left(\frac{1}{2}, \frac{1}{2}\right)\)
- D \((1,1)\)
Answer & Solution
Correct Answer
(C) \(\left(\frac{1}{2}, \frac{1}{2}\right)\)
Step-by-step Solution
Detailed explanation
\(2 x^2-3 x y+y^2=0 \implies (2x-y)(x-y)=0\) Lines are \(L_1: 2x-y=0\), \(L_2: x-y=0\), \(L_3: x+y=1\). Vertices: \(A = L_1 \cap L_2 = (0,0)\). \(B = L_1 \cap L_3: 2x-(1-x)=0 \implies 3x=1 \implies x=1/3, y=2/3 \implies (1/3, 2/3)\).…
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