Question

The equation of the circle which touches both axes and whose center is $(x_1,y_1)$ is

• A. $x^2+y^2+2x_1(x+y)+x_1^2=0$
• B. $x^2+y^2-2x_1(x+y)+x_1^2=0$
• C. $x^2+y^2=x_1^2+y_1^2$
• D. $x^2+y^2+2x{x}_1+2y{y}_1=0$

Answer 1

The correct option is B $x^2+y^2-2x_1(x+y)+x_1^2=0$

Let the radius be $y$

Then,

$E{q}^n:(x-h{)}^2+(y-k{)}^2=r^2$

$\therefore (x-x_1{)}^2+(y-y_1{)}^2=y_1^2$

$x^2+x_1^2-2x{x}_1+y^2+y_1^2-2y{y}_1=y_1^2$

$\therefore x^2+y^2-2x{x}_1-2y{y}_1+x_1^2=0$

$[\therefore x_1=y_1]$

$\therefore x^2+y^2-2x{x}_1-2y{x}_1+x_1^2=0$

$\therefore x^2+y^2-2x_1(x+y)+x_1^2=0$