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  • The locus of centres of family of circles passing through the origin and cutting the circle <img alt="\mathrm{x^2+y^2-4 x+6 y-13=0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7

The locus of centres of family of circles passing through the origin and cutting the circle \mathrm{x^2+y^2-4 x+6 y-13=0} orthogonally is
 

Option: 1

\mathrm{4 x+6 y+13=0}

 


Option: 2

\mathrm{4 x-6 y+13=0}
 


Option: 3

\mathrm{4 x+6 y-13=0}
 


Option: 4

\mathrm{4 x-6 y-13=0}


Answers (1)

best_answer

Let family of circles passing through the origin be \mathrm{x^2+y^2+2 g x+2 f y=0}

It cuts the given circle orthogonally, so that \mathrm{ 4 g-6 f-13=0} Hence locus of centre \mathrm{(-g,-f)} is given by

\mathrm{ 4 x-6 y+13=0 }

Hence option 2 is correct.
 

Posted by

Devendra Khairwa

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