Run hard@thehsc
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- Already did part (i), can someone help me to do part (ii)?
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Q help (1 Viewer)
- Thread starter Run hard@thehsc
- Start date
- Already did part (i), can someone help me to do part (ii)?
5uckerberg
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*Before starting this part of the question break it down into bite-sized pieces.*
Part ii in summary is
Sphere
has equation ^{2}+\left(y-2\right)^{2}+\left(z-5\right)^{2}=1)
Sphere
has equation ^{2}+\left(y-2\right)^{2}+\left(z-2\right)^{2}=12)
Both of them use the fact that^{2}+\left(y-b\right)^{2}+\left(z-c\right)^{2}=r^{2})
, where r is the radius and see the resemblence to a circle which is 2D because a sphere is 3D.
Plus, you need to find the equation of a circle and find its centre and radius. Which one would you do first?
If you look at the context of the question you will see that the centre for the x and y-axis are the same the only change is the z coordinates.
Thus, we will solve for the centre first.
Using what we know start with the fact that
^{2}+\left(y-2\right)^{2}+\left(z-5\right)^{2}-1=\left(x-2\right)^{2}+\left(y-2\right)^{2}+\left(z-2\right)^{2}-12)
Take away^{2}+\left(y-2\right)^{2})
on both sides.
That leaves us with^{2}-\left(z-5\right)^{2}=11)
Using difference of two squares we will have
}=11)
Dividing by 3 we will have
=\frac{11}{3})
.
.
There you have found the centre of the intersection of the two spheres)
.
Now, find the radius.
Draw a diagram that will look something like this.
Part ii in summary is
Sphere
Sphere
Both of them use the fact that
Plus, you need to find the equation of a circle and find its centre and radius. Which one would you do first?
If you look at the context of the question you will see that the centre for the x and y-axis are the same the only change is the z coordinates.
Thus, we will solve for the centre first.
Using what we know start with the fact that
Take away
That leaves us with
Using difference of two squares we will have
Dividing by 3 we will have
There you have found the centre of the intersection of the two spheres
Now, find the radius.
Draw a diagram that will look something like this.
Last edited:
5uckerberg
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Follow the instruction from the diagram and then use the fact that the formula of the circle is ^{2}+\left(y-b\right)^{2}=r^{2})
as the equation of the intersection.
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Run hard@thehsc
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@5uckerberg I used the exact same method - guess just careless mistake in working out!!!
5uckerberg
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WITh the diagram instead of 12 it should be square root of 12.