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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
Find an equation of the sphere that passes through the point (7, 5, -3) and has a center (5, 8, 1).
Solution:
We have equation of sphere centre at (h, k, l) and radius r as (x - h)2 + (y - k)2 + (z - l)2 = r2
Given centre = (h, k, l) = (5, 8, 1) and the sphere passes through a point (7, 5, -3).
Radius = distance between the centre (5, 8, 1) and the point (7, 5, -3).
∴ r = √[(5 - 7)2 + (8 - 5)2 + (1 - (-3))2]
r = √29
Equation of sphere is (x - h)2 + (y - k)2 + (z - l)2 = r2
⇒ (x - 5)2 + (y - 8)2 + (z - 1)2 = (√29)2
⇒ x2 + y2 + z2 -10x -16y - 2z + 25 + 64 + 1 = 29
⇒ x2 + y2 + z2 - 10x - 16y - 2z + 61
Find an equation of the sphere that passes through the point (7, 5, -3) and has a center (5, 8, 1).
Summary:
The equation of the sphere that passes through the point (7, 5, -3) and has a center at (5, 8, 1), is x2 + y2 + z2 - 10x - 16y - 2z + 61.
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