Find equations of the spheres with center(3, −4, 5) that touch the following planes. a. xy-plane b. yz- plane c. xz-plane

By using the general sphere equation and what we know about planes, we will get:

The general sphere of radius R centered in the point (a, b, c) is given by:

(x - a)^2 + (y - b)^2 + (z - c)^2 = R^2

If we want a sphere centered in (3, -4, 5) we will have:

(x - 3)^2 + (y + 4)^2 + (z - 5)^2 = R^2

a) We want the sphere to touch the xy-plane, (with z = 0) then the radius must be at least equal to the z-component of the point, so we have R = 5, then the equation is:

(x - 3)^2 + (y + 4)^2 + (z - 5)^2 = 5^2

b) This time is the yz-plane, so the radius must be equal to the x-component.

(x - 3)^2 + (y + 4)^2 + (z - 5)^2 = 3^2

c) Finally, the xz-plane, this time the radius must be equal to the y-component.

(x - 3)^2 + (y + 4)^2 + (z - 5)^2 = 4^2

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this is the answer for you hope it

a and c

step-by-step explanation: