Answered: Write the equation of a sphere that has…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Concept explainers

Question

Write the equation of a sphere that has a center at C(2, 5,-3) and contains points D(4, 1, 1) on the edge of the sphere

also what is the image of the sphere in the plane x=5

Expert Solution

Step 1

Given Data:

The centre of the sphere is: C(h, j, l)=C(2, 5, -3)

The point at the edge of the sphere is: D(x₀, y₀, z₀)=D(4, 1, 1)

The radius of the sphere is,

$r = \sqrt{{(h - x_{0})}^{2} + {(j - y_{0})}^{2} + {(l - z_{0})}^{2}}$

Substitute the given values in the above equation.

$\begin{array}{rcl} r & = & \sqrt{{(2 - 4)}^{2} + {(5 - 1)}^{2} + {(- 3 - 1)}^{2}} \\ = & \sqrt{{(- 2)}^{2} + {(4)}^{2} + {(- 4)}^{2}} \\ = & \sqrt{4 + 16 + 16} \\ = & \sqrt{36} \\ = & 6 \end{array}$

Step by step

Solved in 3 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Cartesian Coordinates$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions