Find the equation of circle which touches both the negative axes and has its center on the line x-2y=3.?

1 Answer
Oct 23, 2017

(x+3)^2+(y+3)^2=9

Explanation:

The center of the circle must have equal x and y coordinate values if the circle touches both axes.

For the line x-2y=3
this means that (after substituting x for y, since they need to be equal)
color(white)("XXX")x-2x=3color(white)("xxx")rarrcolor(white)("xxx")x=-3
and similarly
color(white)("XXX")y=-3

With a center at (color(green)(-3),color(blue)(-3)) and a radius of color(magenta)3 (since this is the distance from the center to both axes),
the equation of the circle is
color(white)("XXX")(x-(color(green)(-3)))^2+(y-(color(blue)(-3)))^2=color(red)3^2
or
color(white)("XXX")(x+3)^2+(y+3)^2=9

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