Question

Find the equation of director circle of a circle whose equation is $x^2+y^2-4x+6y+12=0$

• A. $x^2+y^2-4x+6y+11=0$
• B. $x^2+y^2-4x+6y+12=0$
• C. $x^2+y^2-2x+3y+11=0$
• D. $x^2+y^2-4x+6y+1=0$

Answer 1

The correct option is A

$x^2+y^2-4x+6y+11=0$

Given circle is $x^2+y^2-4x+6y+12=0$

Center of circle (-g,-f)=(2,-3)

Radiusof circle=$\sqrt{g^2+f^2-c}=\sqrt{4+9-12}=\sqrt{1}=1$

We know, the director circle of a circle is the concentric circle having radius equal to $\sqrt{2}$ times the original circle radius of the director circle of a given circle =$\sqrt{2}\times 1=\sqrt{2}$

Equation of director circle of the given circle

$(x-2{)}^2+(y+3{)}^2=(\sqrt{2}{)}^2$

$x^2+4-4x+y^2+9+6y=2$

$x^2+y^2-4x+6y+11=0$

Option A is correct