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THE CIRCLE
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EXERCISE 3.3
Find the equation of the circle defined by the given condition.
1. Through \( (6,-6),(-1,-5) \) and \( (7,-5) \).
2. Through \( (4,0),(2,-1) \), and \( (1,1) \).
3. Through \( (-6,7) \) and \( (1,8) \), radius 5 .
4. Circumscribes the triangle with vertices \( \mid(1,-4),(3,-2) \) and \( (4,5) \).
5. Inscribed in the triangle whose sides are \( 3 x-4 y=19,4 x+3 y= \) 17 and \( x+7=0 \)
6. Through the origin and \( (-1,-3) \); tangent to \( 2 x+y+10=0 \).
7. Through \( (6,-1) \); tangent to \( 4 x-3 y-2=0 \) at \( (-1,-2) \).
8. Through \( (1,2) \) and \( (3,4) \); center on \( 3 x+y-13=0 \).
9. Through \( (4,2) \) and \( (-6,-2) \), center on the \( y \)-axis.
10. Passes through \( (-1,1) \) and with center at the point of intersection of \( x+3 y+7=0 \) and \( 3 x-2 y-12=0 \)