A MATHS 圓

設圓心的座標為(h,k)。
根據已知條件:
h – 2k + 9 = 0
h = 2k – 9 --- ( 1 )
圓心與(1,-4)的距離 = 圓心與(5,2)的距離 = 半徑
√[ ( h – 1 )2 + ( k + 4 )2 ] = √[ ( h – 5 )2 + ( k – 2 )2 ]
( h – 1 )2 – ( h – 5 )2 = ( k – 2 )2 – ( k + 4 )2
( h – 1 + h – 5 )( h – 1 – h + 5 ) = ( k – 2 + k + 4 )( k – 2 – k – 4 )
( 2h – 6 )( 4 ) = ( 2k + 2 )( - 6 )
( h – 3 )( 2 ) = ( k + 1 )( - 3 )
2h – 6 = - 3k – 3
2h + 3k = 3 --- ( 2 )
代( 1 )入( 2 ),
2( 2k – 9 ) + 3k = 3
4k – 18 + 3k = 3
7k = 21
k = 3
h = 2 ( 3 ) – 9 = -3
圓的半徑: √[ ( -3 – 1 )2 + ( 3 + 4 )2 ] = √65
圓的方程: ( x – h )2 + ( y – k )2 = r2
( x + 3 )2 + ( y – 3 )2 = 65
x2 + 6x + 9 + y2 – 6y + 9 = 65
x2 + y2 + 6x – 6y – 47 = 0