jee-main 2022 Q73

jee-main · India · session2_26jul_shift2 Circles Optimization on a Circle
Let $P$ and $Q$ be any points on the curves $( x - 1 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 1$ and $y = x ^ { 2 }$, respectively. The distance between $P$ and $Q$ is minimum for some value of the abscissa of $P$ in the interval
(1) $\left( 0 , \frac { 1 } { 4 } \right)$
(2) $\left( \frac { 1 } { 2 } , \frac { 3 } { 4 } \right)$
(3) $\left( \frac { 1 } { 4 } , \frac { 1 } { 2 } \right)$
(4) $\left( \frac { 3 } { 4 } , 1 \right)$
Let $P$ and $Q$ be any points on the curves $( x - 1 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 1$ and $y = x ^ { 2 }$, respectively. The distance between $P$ and $Q$ is minimum for some value of the abscissa of $P$ in the interval\\
(1) $\left( 0 , \frac { 1 } { 4 } \right)$\\
(2) $\left( \frac { 1 } { 2 } , \frac { 3 } { 4 } \right)$\\
(3) $\left( \frac { 1 } { 4 } , \frac { 1 } { 2 } \right)$\\
(4) $\left( \frac { 3 } { 4 } , 1 \right)$