Question

let S1=x^2+y^2-2x-6y+9=0 and S2 = x^2+y^2+2y-8=0 be two circles with center C1, C2 and radius R1 and R2 respectively then C1C2+R1+R2 equals

Answer 1

$x^2+y^2+2gx+2fy+c=0$

$C = (-g , -f)$

$r=\sqrt{g^2+f^2-c}$

• $C_1=(1,3)$    

• $R_1 = \sqrt{1+9-9}=\sqrt1=1$

________________________

• $C_2=(-3,1)$

• $R_2=\sqrt{9+1-1}=\sqrt9=3$

________________________

• $C_1C_2=\sqrt{16+4}=\sqrt20=2\sqrt5$

• $R_1+R_2=3+1=4$

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$\boxed{\bold{C_1C_2+R_1+R_2=2\sqrt5+4}}$

Answer 2

Answer:

We know that

x² + y² +2gx +2fy + c = 0 is an equation of a circle with centre at ( - g, - f) & radius √(g²+f²-c)

So For circle S1 :

Centre = C1 = (1,3)

Radius =R1 = √(1²+3²-9) = 1

So For circle S2 :

Centre = C2 = (0,-1)

Radius =R1 = √(0²+1+8) = 3

So C1C2

= Distance between centres

= √ ( 1- 0) ² + ( 3 +1) ²

= √17

So

C1C2+R1+R2 = 4+√17

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