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 \[\left( - 4, 4 \right) and \left( 4, - 4 \right),\]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

\[x^2 + y^2 - 8x + 8y + 16 = 0\]