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| Math Central | Quandaries & Queries |
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Question from isvarya, a student: Find equation of the sphere with centre (1,-4, 3) and radius 5 What is the intersection of this sphere with the xz plane? |
Isvarya,
The distance between two points (x, y, z) and (p, q, r) is the square root of
(x - p)2 + (y - q)2 + (z - r)2
thus a point (x, y, z) is on the sphere with centre (1, -4, 3) and radius 5 if and only if the distance from (x, y, z) to (1, -4, 3) is 52 = 25. Write this equation and simplify it to find the equation of the sphere.
A point on the sphere is on the xz plane if its y-coordinate is zero.
I hope this helps,
Harley
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