- #1
MidgetDwarf
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Write the equation of the sphere with radius 7 and center on the positive z-axis, if the sphere is tangent to the plane z=0.
I know this is an easy problem if i understood the terminology better.
The equation of a sphere (x-h)^2 +(y-k)^2 +(z-l)^2 = 49.
I know that the plane z is the set S={(x,y,0)| z=0}, it is a plane parallel to the xy-axis (vertical plane).
What does it mean by, " with radius 7 and center on the positive z-axis"?
Is it x^2+y^2 +(z-l)^2=49 ?
I am not sure how to proceed.
At first i used the equation of the sphere.
(x-h)^2 +(y-k)^2 +(z-l)^2 = 49.
and I let h=x k=y and z=0 (points taken from the plane)
I end up with (-l)^2=49
l=7.
I need a new equation representing the the tangent from the sphere and plane.
can I say x^2 +y^2 +(z-7)^2= 49? It is the answer in the back of the book.
My argument looks very weak and flawed.
I know this is an easy problem if i understood the terminology better.
The equation of a sphere (x-h)^2 +(y-k)^2 +(z-l)^2 = 49.
I know that the plane z is the set S={(x,y,0)| z=0}, it is a plane parallel to the xy-axis (vertical plane).
What does it mean by, " with radius 7 and center on the positive z-axis"?
Is it x^2+y^2 +(z-l)^2=49 ?
I am not sure how to proceed.
At first i used the equation of the sphere.
(x-h)^2 +(y-k)^2 +(z-l)^2 = 49.
and I let h=x k=y and z=0 (points taken from the plane)
I end up with (-l)^2=49
l=7.
I need a new equation representing the the tangent from the sphere and plane.
can I say x^2 +y^2 +(z-7)^2= 49? It is the answer in the back of the book.
My argument looks very weak and flawed.