Precalculus Help: Find the Equation of a Circle Tangent to a Line

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In summary: Determine the equation (in general form) of the circle.Normally I can do this sort of problem but I am having a hard time with this one. I don't know how to determine the center point or radius...frustrating.. Thanks, Jennifer
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JeNNeHJo
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I was wondering if anyone could help me with this problem

A circle is tanget to line 2x-y+1=0, at point (2, 5), and the center point is on line, x+y=9. Determine the equation (in general form) of the circle.

Normally I can do this sort of problem but I am having a hard time with this one. I don't know how to determine the center point or radius...frustrating..


Thanks, Jennifer
 
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  • #2
JeNNeHJo said:
I was wondering if anyone could help me with this problem

A circle is tanget to line 2x-y+1=0, at point (2, 5), and the center point is on line, x+y=9. Determine the equation (in general form) of the circle.

Normally I can do this sort of problem but I am having a hard time with this one. I don't know how to determine the center point or radius...frustrating..


Thanks, Jennifer
This might be wrong because I'm basically an idiot, but here's what I'd do,…

Write an equation for a line that is orthogonal to 2x-y+1=0 and also passes through point (2,5).

Then solve for where that line and x+y=9 cross. That point must be the center of the circle.

The radius of the circle is the distance between those two points and the rest is history, … Er,.. I mean, mathematics.

I think that'll do it, but I'm sure some real mathematicians will come along and correct me if I'm wrong. :wink:
 
  • #3
NeutronStar said:
This might be wrong because I'm basically an idiot, but here's what I'd do,…

Write an equation for a line that is orthogonal to 2x-y+1=0 and also passes through point (2,5).

Then solve for where that line and x+y=9 cross. That point must be the center of the circle.

The radius of the circle is the distance between those two points and the rest is history, … Er,.. I mean, mathematics.

I think that'll do it, but I'm sure some real mathematicians will come along and correct me if I'm wrong. :wink:

That's what I would've done.
 
  • #4
hello,

i just starting taking classes for pre-cal... haven't taken classes in yrs... besides the calculator and the textbook - what else can i buy to help me with this class? any tools?? (besides a tutor)

Thanks in advance!

A
 

1. What is the formula for finding the equation of a circle tangent to a line?

The formula for finding the equation of a circle tangent to a line is (x - a)^2 + (y - b)^2 = r^2, where (a,b) is the center of the circle and r is the radius.

2. How do I find the coordinates of the center of the circle?

To find the coordinates of the center of the circle, you will need to use the equation of the line and the distance formula. First, find the slope of the line and then use the perpendicular slope to find the slope of the line that passes through the center of the circle. Then, use the distance formula to find the distance between the center of the circle and the given line. Finally, use the midpoint formula to find the coordinates of the center.

3. Can I use any point on the line to find the equation of the circle?

No, you cannot use any point on the line to find the equation of the circle. You will need to use a point that is equidistant from the given line. This point will be the center of the circle.

4. How do I find the radius of the circle?

To find the radius of the circle, you will need to use the distance formula. The distance between the center of the circle and any point on the circle will be equal to the radius.

5. Can I use this formula for any line and circle combination?

Yes, you can use this formula for any line and circle combination as long as the line and the circle are tangent to each other. However, if the line and the circle are not tangent, this formula will not work.

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