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

If you want to learn more about spheres, you can read:

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not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this

i believe that the answer is

b. y-1=-2(x-4)

hope this !