Math CentralQuandaries & Queries


Question from Eric, a student:

Hi I am trying to complete a packet that has a list of questions to brush up on pre-calculus skills. The question asks "For the circle x^2 +y^2 + 6x - 4y + 3 = 0 find : the equation of the tangent at (-2,5). I have already found the equation for the circle and standard form and the center and radius. However, i do not know how to find the slope or y-intercept of the tangent line. Please help. Thanks.

Hi Eric.

If you have the center of the circle and a point on it, then the line connecting them is a radius. You can find the slope of that line and the tangent is perpendicular to it (the tangent line is always perpendicular to the radius at the point of tangency).

Then, with the slope and the point known, you can quickly write the equation of that line.

Stephen La Rocque.

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