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  • Let <img alt="\mathrm{\mathrm{S}_1 \text { and } \mathrm{S}_2}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5Cmathrm%7BS%7D_1%20%5Ctext%20%7B%20and%

Let \mathrm{\mathrm{S}_1 \text { and } \mathrm{S}_2} be two variable circles whose centres lie on different members of family of circles \mathrm{x^2+y^2-2 x \cos \theta-2 y \sin \theta-3=0} and pass through a fixed point \mathrm{(9, \sqrt{243})}. The maximum difference of the radii of \mathrm{\mathrm{S}_1 \text { and } \mathrm{S}_2} is

 

Option: 1

6


Option: 2

8


Option: 3

12


Option: 4

none of these

 


Answers (1)

best_answer

Distance between variable radii of two circles passing through a fixed point will be maximum when the fixed point and respective centres are collinear. So maximum difference of radius will be 6.

Posted by

himanshu.meshram

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