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  • The equation of the radical axis of the two circles <img alt="\mathrm{7 x^{2}+7 y^{2}-7 x+14 y+18=0\: and \: 4 x^{2}+4 y^{2}-7 x+8 y+20=0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cm

The equation of the radical axis of the two circles \mathrm{7 x^{2}+7 y^{2}-7 x+14 y+18=0\: and \: 4 x^{2}+4 y^{2}-7 x+8 y+20=0} is given by

Option: 1

\mathrm{3 x^{2}+3 y^{2}-6 y-2=0}


Option: 2

\mathrm{21 x-68=0}


Option: 3

\mathrm{x-2 y-5=0}


Option: 4

None of these.


Answers (1)

best_answer

Here, \mathrm{C_{1}{ }^{\circ}(2,4), r_{1}=\sqrt{2^{2}+4^{2}-0}=2 \sqrt{5}}

\mathrm{and \: \mathrm{C}_{2}{ }^{\circ}(4,3), \mathrm{r}_{2}=\sqrt{4^{2}+3^{2}-20}=\sqrt{5}}

\mathrm{Now, C_{1} C_{2}=\sqrt{(4-2)^{2}+(3-4)^{2}}=\sqrt{4+1}=\sqrt{5}=r_{1}-r_{2}}

This shows that these circles touch each other internally.

Hence (B) is the correct answer.

Posted by

Ritika Jonwal

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