The equation of the sphere touching the three | vedclass

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(B) sphere touching the three coordinate planes has its center at $(a, a, a)$ and radius $a$ (assuming the sphere is in the first octant).The standard

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$x^2 + y^2 + z^2 - 2a(x + y + z) + 2a^2 = 0$

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(B) sphere touching the three coordinate planes has its center at $(a, a, a)$ and radius $a$ (assuming the sphere is in the first octant).The standard equation of a sphere with center $(h, k, l)$ and radius $r$ is $(x - h)^2 + (y - k)^2 + (z - l)^2 = r^2$.Substituting the center $(a, a, a)$ and radius $r = a$,we get:$(x - a)^2 + (y - a)^2 + (z - a)^2 = a^2$Expanding the squares:$(x^2 - 2ax + a^2) + (y^2 - 2ay + a^2) + (z^2 - 2az + a^2) = a^2$Simplifying the equation:$x^2 + y^2 + z^2 - 2ax - 2ay - 2az + 3a^2 = a^2$$x^2 + y^2 + z^2 - 2a(x + y + z) + 2a^2 = 0$Thus,the required equation is $x^2 + y^2 + z^2 - 2a(x + y + z) + 2a^2 = 0$.

The equation of the sphere touching the three coordinate planes is

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