AP EAMCET · Maths · Pair of Lines
If two sides of a triangle are represented by \(3 x^2-5 x y+2 y^2=0\) and its orthocentre is \((2,1)\), then the equation of the third side is
- A \(2 x+y-4=0\)
- B \(6 x+3 y-13=0\)
- C \(8 x+4 y-17=0\)
- D \(10 x+5 y-21=0\)
Answer & Solution
Correct Answer
(D) \(10 x+5 y-21=0\)
Step-by-step Solution
Detailed explanation
\(3 x^2-5 x y+2 y^2=0 \implies (x-y)(3x-2y)=0\) Sides are \(L_1: x-y=0\) and \(L_2: 3x-2y=0\). Vertex \(A\) (intersection of \(L_1, L_2\)): \(x-y=0, 3x-2y=0 \implies A(0,0)\). Orthocentre \(H(2,1)\). Altitude from \(A\) to the third side is line \(AH\). Slope of…
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