JEE Main 2023 (Online) 10th April Evening ShiftQuestion 1
Let $A$ be the point $(1,2)$ and $B$ be any point on the curve $x^{2}+y^{2}=16$. If the centre of the locus of the point $P$, which divides the line segment $AB$ in the ratio $3:2$ is the point $C(\alpha,\beta)$, then the length of the line segment $AC$ is
Circle
Solution
$P=\frac{3B+2A}{5}$ with $|B|=4$, so $P$ lies on a circle of centre $C=\frac{2A}{5}=(\tfrac25,\tfrac45)$ and radius $\tfrac{12}{5}$. $AC=\tfrac35|A|=\tfrac{3\sqrt5}{5}$. Option (A).