isi-entrance 2021 Q28

isi-entrance · India · UGA Circles Optimization on a Circle
If two real numbers $x$ and $y$ satisfy $( x + 5 ) ^ { 2 } + ( y - 10 ) ^ { 2 } = 196$, then the minimum possible value of $x ^ { 2 } + 2 x + y ^ { 2 } - 4 y$ is
(A) $271 - 112 \sqrt { 5 }$.
(B) $14 - 4 \sqrt { 5 }$.
(C) $276 - 112 \sqrt { 5 }$.
(D) $9 - 4 \sqrt { 5 }$.
If two real numbers $x$ and $y$ satisfy $( x + 5 ) ^ { 2 } + ( y - 10 ) ^ { 2 } = 196$, then the minimum possible value of $x ^ { 2 } + 2 x + y ^ { 2 } - 4 y$ is\\
(A) $271 - 112 \sqrt { 5 }$.\\
(B) $14 - 4 \sqrt { 5 }$.\\
(C) $276 - 112 \sqrt { 5 }$.\\
(D) $9 - 4 \sqrt { 5 }$.