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
\(2x^2-3xy+y^2=0 \implies (2x-y)(x-y)=0\) \(L_1: y=x\) \(L_2: y=2x\) \(L_3: x+y=1\) Slope of \(L_1\), \(m_1=1\) Slope of \(L_3\), \(m_3=-1\) \(m_1 \cdot m_3 = 1 \cdot (-1) = -1\) \(L_1 \perp L_3\) The orthocentre is the vertex formed by the intersection of \(L_1\) and \(L_3\).…
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