You can put this solution on YOUR website! The line y=7x+7 is a chord of the circle x^2 + y^2-6x-6y-7=0, find the length of the chord.
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x^2 + y^2-6x-6y-7=0
complete the squares
(x^2-6x+9)+(y^2-6y+9)=7+9+9=25
(x-3)^2+(y-3)^2=25
..
(y-3)^2=(7x+7-3)^2=(7x+4)^2=49x^2+56x+16
(x-3)^2+(y-3)^2=x^2-6x+9+49x^2+56x+16=50x^2+50x+25
..
50x^2+50x+25=25
50x^2+50x=0
x^2+x=0
x(x+1)=0
x=0 and x=-1
..
y=7x+7=0+7=7
y=-7+7=0
..
points of intersection: (0,7) and (-1,0)
Using distance formula:
d^2=(x1-x2)^2+(y1-y2)^2
d^2=(0+1)^2+(7-0)^2
d^2=1+49=50
d=√50≈7.07
ans:
The length of the chord≈7.07
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