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

  1. #1
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    equation of circle w/ center at (-7, -4), tangent to x-axis

    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.

  2. #2
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    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.

  3. #3
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    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.

  4. #4
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    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!

  5. #5
    Elite Member
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    Sketch the problem.

    Drop a perpendicular from the center to the tangent line.

    Then think some more....
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

  6. #6
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    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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