equation of circle w/ center at (-7, -4), tangent to x-axis

J

jshaziza

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Jan 26, 2007
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Find the equation of a circle with a center at (-7,-4) and tangent to the x-axis.

I am having trouble understanding and solving this problem.

For a similar problem, I had to find the equation of a circle with center at (4, 5) and radius 6. For this problem I used standard form and solved as (x - 4)^2 + (y - 5)^2 = 36. But I can't figure out how to take this concept and solve for the first equation. Thx. for any help.
 
It is only slightly different from the one you solved. They just told you the radius in a different way. If the center is (-7,-4), the center is 4 from the x-axis. Tell me why that is so and tell me how that helps find the radius.
 
Well the center is four from the x-axis because it tells me that it is tangent to the x-axis which means that the outermost point is on the x-axis.

Your second question I am not so sure, would it be that knowing this information I know a point on the line, which will help me figure the radius out, and if so how do I know which point on the x-axis to choose from? Thx. for your help.
 
You know that the center of the circle is (-7, -4).

And, you know that the distance from the x-axis (measured on a perpendicular from the center to the x-axis) is 4 units.

Given the center and the radius, you've already demonstrated that you know how to write the equation of the circle using (x - h)<SUP>2</SUP> + (y - k)<SUP>2</SUP> = r<SUP>2</SUP>

So...DO it!
 
Sketch the problem.

Drop a perpendicular from the center to the tangent line.

Then think some more....
 
Sorry, my bad you guys, I thought the information given to me had to do with a point on the line of the circle which I would than use the hard way to find the radius. But now I realize that 4 is the actual radius. Thx. again for your help.
 
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