TS EAMCET · Maths · Straight Lines
The centroid of a variable triangle \(A B C\) is at the distance of 5 units from the origin. If \(A=(2,3)\) and \(B=(3,2)\), then the locus of \(C\) is
- A a circle of radius 225 units
- B a rectangular hyperbola
- C a circle of diameter 30 units
- D an ellipse with eccentricity \(\frac{4}{5}\)
Answer & Solution
Correct Answer
(C) a circle of diameter 30 units
Step-by-step Solution
Detailed explanation
Let \(C\) be \((h, k)\) \(\begin{aligned} & \text { Centroid }=\left(\frac{2+3+h}{3}, \frac{3+2+k}{3}\right)=\left(\frac{5+h}{3}, \frac{5+k}{3}\right) \\ & \Rightarrow\left(\frac{5+h}{3}\right)^2+\left(\frac{5+k}{3}\right)^2=25 ;(x+5)^2+(y+5)^2=225 \end{aligned}\) This is an…
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