Q81 / 160 · TS EAMCET 2024 (09 May Shift 1) · Mathematics
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
- Aa circle of radius 225 units
- Ba rectangular hyperbola
- Correct answerCa circle of diameter 30 units
- Dan ellipse with eccentricity $\frac{4}{5}$
Solution
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 equation of circle. $\begin{aligned} & \text { Radius }=\sqrt{225}=15 \\ & \text { Diameter }=30 . \end{aligned}$
This is an equation of circle. $\begin{aligned} & \text { Radius }=\sqrt{225}=15 \\ & \text { Diameter }=30 . \end{aligned}$
Hence, the correct answer is option: 'C'.