maths(equation of circle2)20pt

a)
L: x-3y-9=0
C :2x²+2y²-18x+6y+25=0
From L, x=3y+9.
Putting x into C:
2(3y+9)²+2y²-18(3y+9)+6y+25=0
4y²+12y+5=0.............(*)
∆ of (*)=12²-4(4)(5)=64>0
∴L cuts C at 2 points.

b)
As roots of (*) are the y-coordinates of the two points of intersection of L and C
∴y-coord of mid-point=sum of roots of (*)/2=(-12/4)/2=-3/2
Putting y=-3/2 into L, x-coord of mid-point=3(-3/2)+9=9/2
∴mid-point=(9/2, -3/2)

圖片參考：http://i1099.photobucket.com/albums/g395/jasoncube/4d75fc76.png


I HOPE THIS CAN HELP YOU! ~ ^_^