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  • If two circles  <img alt="\mathrm{x^2+y^2+2 g x+2 f y=0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bx%5E2&plus;y%5E2&plus;2%20g%20x&plus;2%20f%20y%3D0%7

If two circles  \mathrm{x^2+y^2+2 g x+2 f y=0} and \mathrm{x^2+y^2+2 g_1 x+2 f_1 y=0} 

touch each other, then

Option: 1

\mathrm{g f_1=g_V f}


Option: 2

\mathrm{g g_1+f f_1=0}


Option: 3

\mathrm{g g_1-f f_1=0}


Option: 4

none of these


Answers (1)

best_answer

As both the circles pass through the origin, they will touch each other at the common point O. However, the equations of the tangent to circles at the origin are

\mathrm{\begin{array}{ll} 2 g x+2 f y=0 \\ 2 g_1 x+2 f_1 y=0 \end{array}} ----------(1) and (2)

Equations (1) and (2) represent the same lines if

\mathrm{\frac{g}{g_1}=\frac{f}{f_1} \Rightarrow g f_1=g_V f}

 

 

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vinayak

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