If two circles, x2+y2+2 g1 x+2 f1 y=0 and x2+y2 +2 g2 x+2 f2 y=0 touch each other externally then

Question

If two circles, x2+y2+2 g1 x+2 f1 y=0 and x2+y2 +2 g2 x+2 f2 y=0 touch each other externally then (A) f1 g1=f2 g2 (B) (f1/g1)=(f2/g2) (C) f1 f2=g1 g2 (D) none of these

Tardigrade Admin · Accepted Answer

If two circles touch each other, then C1 C2=r1+r2 ⇒ √(-g1+g2)2+(-f1+f2)2=√g12+f12+√g22+f22 Squaring both sides, we get -2 g1 g2-2 f1 f2=2 √(g12+f12)(g22+f22) Again squaring, we get (g1 f2)2+(g2 f1)2-2 g1 g2 f1 f2=0 ⇒ (g1 f2-g2 f1)2=0 ⇒ (g1/g2)=(f1/f2)

Q. If two circles, $x^{2} + y^{2} + 2 g_{1} x + 2 f_{1} y = 0$ and $x^{2} + y^{2} + 2 g_{2} x + 2 f_{2} y = 0$ touch each other externally then

$f_{1} g_{1} = f_{2} g_{2}$

$\frac{f _{1}}{g _{1}} = \frac{f _{2}}{g _{2}}$

$f_{1} f_{2} = g_{1} g_{2}$

none of these

Q. If two circles, x2+y2+2g1​x+2f1​y=0 and x2+y2+2g2​x+2f2​y=0 touch each other externally then

f1​g1​=f2​g2​

g1​f1​​=g2​f2​​

f1​f2​=g1​g2​

none of these

Q. If two circles, $x^{2} + y^{2} + 2 g_{1} x + 2 f_{1} y = 0$ and $x^{2} + y^{2} + 2 g_{2} x + 2 f_{2} y = 0$ touch each other externally then

$f_{1} g_{1} = f_{2} g_{2}$

$\frac{f _{1}}{g _{1}} = \frac{f _{2}}{g _{2}}$

$f_{1} f_{2} = g_{1} g_{2}$