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  • The locus of the centre of a circle which touches externally the circle <img alt="\mathrm{x 2+y 2-6 x-6 y-14=0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bx%202&plus;y%20

The locus of the centre of a circle which touches externally the circle \mathrm{x 2+y 2-6 x-6 y-14=0} and also touches the \mathrm{y}-axis is given by the equation: 

Option: 1

\mathrm{x^{2}-6 x-10 y+14=0}


Option: 2

\mathrm{x^{2}-10 x-6 y+14=0}


Option: 3

\mathrm{y^{2}-6 x-10 y+14=0}


Option: 4

\mathrm{y^{2}-10 x-6 y+14=0}


Answers (1)

best_answer

Equation of circle touches y- axis is given by \mathrm{(x-4)^{2}+(y-k)^{2}=h^{2}}

Given by  \mathrm{(x-4)^{2}+(y-k)^{2}=h^{2}}
this touches \mathrm{(x-3)^{2}+(y-3)^{2}=4}

\mathrm{\Rightarrow \sqrt{(\mathrm{h}-3)^{2}+(\mathrm{k}-3)^{2}}=\mathrm{h}+2}

Hence locus is
\mathrm{y^{2}-6 y-10 x+14=0}

Hence (D) is the correct answer.

Posted by

Gautam harsolia

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