Question

A circle of radius 4 units touches the coordinate axes in the first quadrant. Find the equations of its images with respect to the line mirrors x = 0 and y = 0.

Answer 1

It is given that a circle of radius 4 units touches the coordinate axes in the first quadrant.

Centre of the given circle = (4, 4)

The equation of the given circle is ${\left(x-4\right)}^2+{\left(y-4\right)}^2=16$.

The images of this circle with respect to the line mirrors x = 0 and y = 0. They have their centres at $\left(-4,4\right)\mathrm{and}\left(4,-4\right),$ respectively.

∴ Required equations of the images = ${\left(x+4\right)}^2+{\left(y-4\right)}^2=16$ and ${\left(x-4\right)}^2+{\left(y+4\right)}^2=16$

= $x^2+y^2+8x-8y+16=0$ and $x^2+y^2-8x+8y+16=0$