Find the equation in the general form of the sphere described

In summary, to find the tangent to the plane x-3y+4z+23=0 at (1,4,-3) with a radius of sqrt(26), you can find a normal to the plane and use it to find the center of the sphere. From there, you can determine the tangent points on the sphere.
  • #1
lolphysics3
9
0

Homework Statement


tangent to x-3y+4z+23=0 at (1,4,-3) with radius sqrt(26)


Homework Equations





The Attempt at a Solution



well i initially thought it's possible to set up a system of equations but it didn't work out.
 
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  • #2
lolphysics3 said:

Homework Statement


tangent to x-3y+4z+23=0 at (1,4,-3) with radius sqrt(26)


Homework Equations





The Attempt at a Solution



well i initially thought it's possible to set up a system of equations but it didn't work out.
Can you find a normal to the plane? It will point toward the center of the sphere (there will be two of them, though). And you know the radius of the sphere, so you should be able to find the center of the sphere.
 

1. What is the general form of the equation for a sphere?

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

2. How do you find the center of a sphere given its equation?

To find the center of a sphere given its equation, you can rewrite the equation in the general form and identify the values of h, k, and l. These values represent the coordinates of the center of the sphere.

3. Can you find the radius of a sphere if you know its equation?

Yes, you can find the radius of a sphere if you know its equation. Simply take the square root of the constant value on the right side of the equation.

4. What information can you obtain from the general form of a sphere's equation?

The general form of a sphere's equation can provide information about the center and radius of the sphere. It can also be used to determine whether a given point is inside, outside, or on the surface of the sphere.

5. How do you graph a sphere from its general form equation?

To graph a sphere from its general form equation, plot the coordinates of the center on a 3D coordinate plane. Then, use the radius to plot points on the surface of the sphere, creating a curved surface. You can also use technology, such as a graphing calculator, to visualize the sphere.

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