Find the equation of the sphere

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In summary, the equation for a sphere is (x - h)^2 + (y - k)^2 + (z - l)^2 = r^2, where (h, k, l) is the center of the sphere and r is the radius. To find the equation of a sphere given specific points, you can use the formula (x - x1)^2 + (y - y1)^2 + (z - z1)^2 = r^2, where (x1, y1, z1) is one of the given points and r is the distance from the center to the point. A sphere is a three-dimensional shape with all points on its surface equidistant from its center, while a
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Find the equation of the sphere centered at (-6,-7,-1) with radius 9.

well i got [tex](x+6)^2 + (y+7)^2 + (z+1)^2-9^2[/tex] which is correct.

now for the next question:

Give an equation which describes the intersection of this sphere with the plane [tex]z=0[/tex].

i don't understand how to do the second question at all, can someone help?
 
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What you got must've been:
[tex](x+6)^2 + (y+7)^2 + (z+1)^2-9^2 = 0[/tex].

The equation that describes the intersection with the plane z = 0 must be:
[tex](x+6)^2 + (y+7)^2 + (0+1)^2-9^2 = (x+6)^2 + (y+7)^2 - 80 = 0 [/tex]
 
  • #3
thanks alot, i get it now
 

What is the equation for a sphere?

The equation for a sphere is (x - h)^2 + (y - k)^2 + (z - l)^2 = r^2, where (h, k, l) is the center of the sphere and r is the radius.

How do you find the equation of a sphere given specific points?

To find the equation of a sphere given specific points, you can use the formula (x - x1)^2 + (y - y1)^2 + (z - z1)^2 = r^2, where (x1, y1, z1) is one of the given points and r is the distance from the center to the point. Repeat this process for at least two other points and then solve the resulting system of equations to find the values of h, k, l, and r in the general sphere equation.

What is the difference between a sphere and a circle?

A sphere is a three-dimensional shape with all points on its surface equidistant from its center. In contrast, a circle is a two-dimensional shape with all points on its circumference equidistant from its center. Essentially, a circle is a flat version of a sphere.

Can the equation of a sphere be written in a different form?

Yes, the equation of a sphere can be rewritten in different forms. For example, the general equation can be expanded and rearranged to get (x^2 + y^2 + z^2) - 2hx - 2ky - 2lz + (h^2 + k^2 + l^2 - r^2) = 0. This form is useful for finding the center and radius of the sphere.

How is the equation of a sphere related to its volume and surface area?

The equation of a sphere is not directly related to its volume and surface area. However, the radius in the equation is the same as the radius used in the formulas for calculating the volume and surface area of a sphere (V = 4/3πr^3 and A = 4πr^2). So, knowing the equation of a sphere can help you find its volume and surface area.

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