Bonjour,
1a)
x²+y²-2x=0
x²-2x+1+y²-1=0
(x-1)²+y²=1
I1=(1;0) R=1
C2 a pour équation (x-2)²+(y-2)²=4
1b)
|I1I2|=√((2-1)²+(2-0)²)=√5 < 1+4
1 c)
[tex]\left \{\begin {array} {ccc}x^2+y^2-2x&=&0\\(x-2)^2+(y-2)^2&=&4\\\end {array} \right.\\\\\\\left \{\begin {array} {ccc}x^2+y^2-2x&=&0\\x+2y=2\\\end {array} \right.\\\\\\\left \{\begin {array} {ccc}y(5y-4)&=&0\\x&=&2-2y\\\end {array} \right.\\\\\\\left \{\begin {array} {ccc}x&=&2\\y&=&0\\\end {array} \right.ou\ \left \{\begin {array} {ccc}x&=&0.4\\y&=&0.8\\\end {array} \right.\\[/tex]
2a)
A1=(0.4,0.8)
A2=(2,0)
mil[A1A2]=(1.2,0.4)
coef directeur de (A1 A2)
[tex]\dfrac{0.8-0}{0.4-2} =-\dfrac{1}{2} \\[/tex]
Equation de la médiatrice :
y-0.4=(x-1.2)*2
y=2x-2
Equation de (I1 I2)
y-0=(x-1)(2-0)/(2-1)
y=2x-2
