좌표평면 위의 두 원
C 1 : ( x − 2 ) 2 + ( y − 6 ) 2 = 1 , C 2 : ( x − 6 ) 2 + ( y − 4 ) 2 = 9 \begin{aligned}C_1:\left(x-2\right)^2+\left(y-6\right)^2=1,\\[6pt]C_2:\left(x-6\right)^2+\left(y-4\right)^2=9\end{aligned} C 1 : ( x − 2 ) 2 + ( y − 6 ) 2 = 1 , C 2 : ( x − 6 ) 2 + ( y − 4 ) 2 = 9 에 대하여 원 C 1 C_1 C 1 P \mathrm{P} P C 2 C_2 C 2 Q \mathrm{Q} Q y y y R \mathrm{R} R S \mathrm{S} S R \mathrm{R} R S \mathrm{S} S x x x R ′ \mathrm{R}' R ′ S ′ \mathrm{S}' S ′ O \mathrm{O} O
ㄱ. 두 점 A ( 4 , 2 ) \mathrm{A}\left(4,\,2\right) A ( 4 , 2 ) A ′ ( 4 , − 2 ) \mathrm{A}'\left(4,\,-2\right) A ′ ( 4 , − 2 ) A R ‾ = A ′ R ′ ‾ \overline{\mathrm{AR}}=\overline{\mathrm{A}'\mathrm{R}'} AR = A ′ R ′
ㄴ. 점 A ( 4 , 2 ) \mathrm{A}\left(4,\,2\right) A ( 4 , 2 ) A R ‾ + P R ′ ‾ \overline{\mathrm{AR}}+\overline{\mathrm{PR}'} AR + PR ′ 9 9 9
ㄷ. 점 B ( a , 6 a + 1 ) \mathrm{B}\left(a,\,6a+1\right) B ( a , 6 a + 1 ) a a a
( B R ‾ + P R ′ ‾ 의 최솟값 ) = ( B S ‾ + Q S ′ ‾ 의 최솟값 ) + 2 \left(\overline{\mathrm{BR}}+\overline{\mathrm{PR}'}\text{의 최솟값}\right)=\left(\overline{\mathrm{BS}}+\overline{\mathrm{QS}'}\text{의 최솟값}\right)+2 ( BR + PR ′ 의 최솟값 ) = ( BS + QS ′ 의 최솟값 ) + 2 일 때, O B ‾ \overline{\mathrm{OB}} OB 65 2 \dfrac{\sqrt{65}}{2} 2 65
