equation of tangent of circle
Let the point of tangency be . Then the slope of radius with end point is , whence, according to the parent entry (http://planetmath.org/TangentOfCircle), its opposite inverse is the slope of the tangent, being perpendicular to the radius. Thus the equation of the tangent is written as
Removing the denominator and the parentheses we obtain from this first , and then
since satisfies (1).
Remark. In the equation (2) of the tangent, , are the coordinates of the point of tangency and the coordinates of an arbitrary point of the tangent line. But one can of course swap those meanings; then we interprete (2) such that , are the coordinates of some point outside the circle (1) and the coordinates of the point of tangency of either of the tangents which may be drawn from to the circle. If (2) now is again interpreted as an equation of a line (its degree (http://planetmath.org/AlgebraicEquation) is 1!), this line must pass through both the mentioned points of tangency and (they satisfy the equation!); in a , (2) is now the equation of the tangent chord of . See also http://mathworld.wolfram.com/Polar.htmlpolar.
|Title||equation of tangent of circle|
|Date of creation||2013-03-22 18:32:16|
|Last modified on||2013-03-22 18:32:16|
|Last modified by||pahio (2872)|