Question

Image of $(x+2{)}^2+(y-3{)}^2=25$ w.r.t. $y=x$, is

• A. $(x-3{)}^2+(y-2{)}^2=25$
• B. $(x-3{)}^2+(y+2{)}^2=25$
• C. $(x+2{)}^2+(y+3{)}^2=25$
• D. $(x-2{)}^2+(y-3{)}^2=25$

Answer 1

The correct option is B $(x-3{)}^2+(y+2{)}^2=25$

The center of the given circle is $(-2,3)$ and it's radius is $5$.
The image of the point $(-2,3)$ in the line $y=x$ is $(x_1,y_2)=(3,-2)$.
The equation of a circle with the center $(x_1,y_2)$ and radius $r$ is given by
$(x-x_1{)}^2+(y-y_1{)}^2=r^2$
The equation of the image circle is $(x-3{)}^2+(y+2{)}^2=25$.