Find an equation for each sphere that passes through the point(5,1,4) and is tangent to all three coordinate planes.

Taliyah Reyes 2022-08-03 Answered
Find an equation for each sphere that passes through the point(5,1,4) and is tangent to all three coordinate planes.
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (2)

kunstboom8w
Answered 2022-08-04 Author has 8 answers
the general sphere equation is
( x x 0 ) 2 + ( y y 0 ) 2 + ( z z 0 ) 2 = R 2 ...(1)
( x 0 , y 0 , z 0 ) is the centerof sphere
since the sphere tangent to all three coordinate planes, we have:
x 0 = y 0 = z 0 = R
(1) change to:
( x R ) 2 + ( y R ) 2 + ( z R ) 2 = R
sphere passes through the point (5,1,4) , we have:
( 5 R ) 2 + ( 1 R ) 2 + ( 4 R ) 2 = R
25 10 R + R 2 + 1 2 R + R 2 + 16 8 R + R 2 = R 2
2 R 2 20 R + 32 = 0
R 2 10 R + 16 = 0
(R-2)(R-8) = 0
R=2, or R=8
the sphere equations are
( x 2 ) 2 + ( y 2 ) 2 + ( z 2 ) 2 = 2 2
or
( x 8 ) 2 + ( y 8 ) 2 + ( z 8 ) 2 = 8 2
Not exactly what you’re looking for?
Ask My Question
popljuvao69
Answered 2022-08-05 Author has 2 answers
everything answered above is totally perfect except that 25+1+16=42, and not 25+1+16=32. So, radius equals 3 and 7.
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-06-11
Find the area of the parallelogram with vertices A(-3, 0), B(-1, 5), C(7, 4), and D(5, -1).
asked 2021-08-19
A curve is given by the following parametric equations. x=20cost,y=10sint.
The parametric equations are used to represent the location of a car going around the racetrack.
a) What is the cartesian equation that represents the race track the car is traveling on?
b) What parametric equations would we use to make the car go 3 times faster on the same track?
c) What parametric equations would we use to make the car go half as fast on the same track?
asked 2020-11-06
Write parametric, equations for the given curve for the given definitions y= 4x + 1 a) x=t b) x= t2 c) x= 4t
asked 2021-09-08

Find a basis for the eigenspace corresponding to the eigenvalue of A given below.
A=[402042100341702283],λ=3

asked 2020-10-28
Consider the helix represented investigation by the vector-valued function r(t)= < 2 cos t, 2 sin t, t >. Solve for t in the relationship derived in part (a), and substitute the result into the original set of parametric equations. This yields a parametrization of the curve in terms of the arc length parameter s.
asked 2022-03-29

Find a vector function that represents the curve of intersection of the two surfaces of the cylinder x^2+y^2=4 and the surface z=xy.

asked 2021-11-21
Find the volume of the solid generated by revolving the standed region about the x-axis.

Te volume of the solid is ? cubic units.
The equation: 4x+3y=24