The line x=y touches a circle at the point (1,1).


The line $x=y$ touches a circle at the point $(1,1)$. If the circle also passes through the point $(1,-3)$, then its radius is :

  1. $3 \sqrt{2}$

  2. 3

  3. $2 \sqrt{2}$

  4. 2

Correct Option: , 3


Equation of circle can be written as $(\mathrm{x}-1)^{2}+(\mathrm{y}-1)^{2}+\lambda(\mathrm{x}-\mathrm{y})=0$

It passes through $(1,-3)$

$16+\lambda(4)=0 \Rightarrow \lambda=-4$

So $(x-1)^{2}+(y-1)^{2}-4(x-y)=0$

$\Rightarrow x^{2}+y^{2}-6 x+2 y+2=0$

$\Rightarrow r=2 \sqrt{2}$

Leave a comment


Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now