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  • The maximum radius of the circle having pair of lines <img alt="\mathrm{y^2+x y-2 x-5 y+6=0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7By%5E2&plus;x%20y-2%20x-5%20y&p

The maximum radius of the circle having pair of lines \mathrm{y^2+x y-2 x-5 y+6=0} as its normals and having the size just sufficient to be contained in the circle \mathrm{x(x-4)+y(y-3)=0} is
 

Option: 1

\mathrm{ \frac{1}{2}}


Option: 2

\frac{5-\sqrt{5}}{2}


Option: 3

1


Option: 4

\frac{\sqrt{5}}{2}


Answers (1)

best_answer


Pair of lines is \mathrm{(y-2)(x+y-3)=0}. centre of circle is the point of intersection of lines \mathrm{y=2}, and \mathrm{\mathrm{x}+\mathrm{y}-3=0 \Rightarrow(1,2)} if radius of required circle is \mathrm{r} ; \mathrm{r}_1-\mathrm{r}=\mathrm{C}_1 \mathrm{C}_2

\mathrm{\frac{5}{2}-r=\sqrt{(1-2)^2+\left(2-\frac{3}{2}\right)^2} \Rightarrow r=\frac{5-\sqrt{5}}{2} }
 

Posted by

SANGALDEEP SINGH

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