Question

If $(1,2),(4,3)$ are the limiting points of coaxial system,then the equation of the circle in its conjugate system having minimum area is

• A. $x^2+y^2-5x-5y+10=0$
• B. $x^2+y^2-8x-6y+25=0$
• C. $x^2+y^2-2x-2y+10=0$
• D. $x^2+y^2+5x+5y-10=0$

Answer 1

The correct option is A $x^2+y^2-5x-5y+10=0$

Equation of radical axis of coaxial system whose limiting points
are $(1,2)$ and $(4,3)$ is
$(y-\frac{1}{2})=-3(x-\frac{5}{2})$
$y+3x=10$
$P=(\frac{5}{2},\frac{5}{2})$
So, equation of circle in conjugate system with minimum area is
$(x-\frac{5}{2}{)}^2+(y-\frac{5}{2}{)}^2=(AP{)}^2=(\frac{\sqrt{10}}{2}{)}^2=\frac{5}{2}$
$x^2+y^2-5x-5y+\frac{25}{2}-\frac{5}{2}=0$
$\Rightarrow x^2+y^2-5x-5y+10=0$