Question

The equation of the circle with centre at $(1,1)$ and touching the line $3x+4y+3=0$ is :

• A. $x^2+y^2-2x-2y+2=0$
• B. $x^2+y^2-2x-2y-2=0$
• C. $x^2+y^2+2x+2y+2=0$
• D. $x^2+y^2-2x+2y-2=0$
• E. $x^2+y^2+2x+2y+4=0$

Answer 1

Answer: (B)

$x^2+y^2-2x-2y-2=0$

Given, centre is $(1,1)$ and line is $3x+4y+3=0$
Radius $=$ distance from centre to the line
$=\frac{|3\times 1+4\times 1+3|}{\sqrt{3^2+4^2}}=\frac{3+4+3}{\sqrt{9+16}}$
$=\frac{10}{5}=2$
Therefore, required equation of circle is
$(x-1{)}^2+(y-1{)}^2=2^2$
$\Rightarrow x^2-2x+1+y^2-2y+1=4$
$\Rightarrow x^2+y^2-2x-2y-2=0$