If two circles, x^2 + y^2 + 2 g₁x + 2 f₁y = 0, & ,x^2 + y^2 + 2 g₂x + 2 f₂y = 0 touch ea

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10-1.Circle and System of Circles

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If the two circles, $x^2 + y^2 + 2 g_1x + 2 f_1y = 0\, \& \,x^2 + y^2 + 2 g_2x + 2 f_2y = 0$ touch each then:

A

$f_1 g_1 = f_2 g_2$

B

$\frac{{{f_1}}}{{{g_1}}} = \frac{{{f_2}}}{{{g_2}}}$

C

$f_1 f_2 = g_1 g_2$

D

none

Solution

circles can touch only at $(0, 0)$

$\Rightarrow \, (-g, -f_1); (0, 0)$ and $(-g_2, -f_2)$ collinear $\Rightarrow \frac{{{f_1}}}{{{g_1}}} = \frac{{{f_2}}}{{{g_2}}}$

Standard 11

Mathematics

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