AP EAMCET · Maths · Straight Lines
If \((a, b)\) is the centroid of the triangle formed by the lines \(4 x^2-17 x y+4 y^2=0\) and \(x+y-5=0\) and \(c\) is the numerical value of the area of the triangle, then \(a+b+c=\)
- A \(\frac{25}{6}\)
- B \(\frac{25}{3}\)
- C \(\frac{65}{6}\)
- D \(\frac{15}{3}\)
Answer & Solution
Correct Answer
(C) \(\frac{65}{6}\)
Step-by-step Solution
Detailed explanation
\(4x^2-17xy+4y^2=0 \implies (4x-y)(x-4y)=0\) Lines are: \(L_1: 4x-y=0\), \(L_2: x-4y=0\), \(L_3: x+y-5=0\) Vertices: \(V_1 = L_1 \cap L_2 = (0,0)\) \(V_2 = L_1 \cap L_3: y=4x \implies x+4x-5=0 \implies 5x=5 \implies x=1, y=4 \implies (1,4)\)…
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