AP EAMCET · Maths · Straight Lines
A variable line passing through a fixed point \((\alpha, \beta)\) intersects the coordinate axes at \(A\) and \(B\). If \(O\) is the origin, then the locus of the centroid of the \(\triangle O A B\) is
- A \(\beta x+\alpha y-2 \alpha \beta=0\)
- B \(\beta x+\alpha y-3 x y=0\)
- C \(\alpha x+\beta y-\left(\alpha^2+\beta^2\right)=0\)
- D \(\beta x+c y+3 x y=0\)
Answer & Solution
Correct Answer
(B) \(\beta x+\alpha y-3 x y=0\)
Step-by-step Solution
Detailed explanation
Let points \(A(a, 0)\) and \(B(0, b)\), so equation of variable line is \[ \frac{x}{a}+\frac{y}{b}=1 \] Since the variable line (i) passes through the point \((\alpha, \beta)\) So, \[ \frac{\alpha}{a}+\frac{\beta}{b}=1 \] Now, centroid of \(\triangle O A B\) is…
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