Question

The equation of circle with centre (1, 2) and tangent x + y - 5 = 0 is

• A. $x^2+y^2+2x-4y+6=0$
• B. $x^2+y^2-2x-4y+3=0$
• C. $x^2+y^2-2x+4y+8=0$
• D. $x^2+y^2-2x-4y+8=0$

Answer 1

The correct option is B $x^2+y^2-2x-4y+3=0$

Radius of circle = perpendicular distance of tangent from the centre of circle

$\Rightarrow r=\frac{1+2-5}{\sqrt{1+1}}=\sqrt{2}$

Hence the equation of required circle is
$(x-1{)}^2+(y-2{)}^2=(\sqrt{2}{)}^2$
$\Rightarrow x^2+y^2-2x-4y+3=0.$