Need to get an equation for when it is tangent

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In summary, the conversation is about finding the equation for a sphere tangent to the yz-plane, given a center point. The speaker is unsure of which coordinate to use and how to find the radius, but knows the general formula for a sphere. They also mention using the distance formula and finding a single point on the yz-plane that is also on the sphere.
  • #1
bharp24
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I need someone to help me! i have been given a center point of (3,-1,-2) of a sphere and i need to get an equation for when it is tangent to the a) the yz plane b) y=7. i know i need to use the distance formuala to attain the radius, but i am majorly confusing myself in what coordinate to pick. Do i just use (0,0,0) as tangent point to the plane for a)?? please help!
 
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  • #2
What is the general formula for a sphere?
 
  • #3
what i have so far is (x-3)^2 + (x+1)^2 + (x+2)^2= r^2. i just need to find the radius of this equation, so that the sphere will be tangent to the yz plane. once i know the coordinates to use for the tangent point, i can use the distance formula to give me the radius.
 
  • #4
It would actually be ...

[tex](x-3)^2+(y+1)^2+(z+2)^2=r^2[/tex]

If you want it tangent to the yz-plane, what variable must be 0?
 
  • #5
that is what i meant..sorry. i still need to know what the equation would be though to figure out when it is tangent to the yz plane.
 
  • #6
So you want a single point to be on the yz plane. What is the equation of the yz plane?
At what point of the sphere is that equation true? What is the distance between that point and the center of the sphere?
 

1. What is the definition of a tangent line?

A tangent line is a straight line that touches a curve at only one point, without crossing through the curve.

2. How do you find the equation for a tangent line?

To find the equation for a tangent line, you first need to find the derivative of the curve at the point where the tangent line needs to be drawn. Then, using the slope of the tangent line and the coordinates of the point, you can use the point-slope form of a line to write the equation.

3. Can a curve have more than one tangent line at a given point?

No, a curve can have only one tangent line at a given point. This is because the tangent line represents the instantaneous rate of change of the curve at that point, and the rate of change can only have one value at a given point.

4. How is the equation for a tangent line useful?

The equation for a tangent line can be used to find the slope of the curve at a specific point, which can help in understanding the behavior of the curve. It is also useful in finding the maximum or minimum values of a curve, as these occur at points where the tangent line is horizontal (slope = 0).

5. Can the equation for a tangent line be used to find the exact value of a curve at a given point?

No, the equation for a tangent line only gives the slope of the curve at a given point. To find the exact value of the curve at that point, you would need to use the original equation of the curve and substitute the x-coordinate of the point.

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