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    Gradient and equation of tangent

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    Say I have for example a circle with centre C(7,-5) passing through point A(6,-3)
    (With tangent line and radius, AC, being perpendicular.)

    1. How would I go about finding the gradient of the tangent?
    2. How would I go about finding that the equation of the tangent at A is the line x=2y+12 ?
    3. And how would I go about finding out that this line meets a second circle with
    equation of x squared -24x +y squared +10y +149=0 in only one point?

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    https://brainmass.com/math/graphs-and-functions/gradient-equation-tangent-57054

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    Please see the attached file.

    Say I have for example a circle with centre C(7,-5) passing through point A(6,-3)
    (With tangent line and radius, AC, being perpendicular.)

    1. How would I go about finding the gradient of the tangent?
    First, we can compute the slope of the line CA, denoted by k,

    So, the slope of the ...

    Solution Summary

    This shows how to find gradient and equation of a tangent to a circle.

    $2.49

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