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 August 30th, 2013, 04:58 AM #1 Senior Member   Joined: Sep 2011 Posts: 395 Thanks: 0 The Equation of a Tangent to a Circle For this question, my final answer in (ii) almost matches that of the books answer. Can anyone confirm if I have the correct answer, or if the book is incorrect? Many thanks. Q. A circle has centre (3, 5) & touches the line . (i) Find the equation of this circle, (ii) Find the equation of the tangent to the circle at the point (1, 4). Attempt: (i) Distance between c & T: Equation of circle: (ii) Equation of line at (1, 4): Distance between c & T: For Ans: (ii) (From text book): August 30th, 2013, 07:20 AM #2 Senior Member   Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: The Equation of a Tangent to a Circle If I we going to work part (ii), I would let the tangent line be: Substituting this into the equation of the circle: Arrange as quadratic in : Equate the discriminant to zero since there is only 1 real root (repeated): The reduces to: And so and the tangent line is: This is what your textbook has. Your error came from using the wrong point in the point-slope formula at the beginning of your working. You used the point (5,4) instead of (1,4). August 30th, 2013, 07:48 AM #3 Senior Member   Joined: Sep 2011 Posts: 395 Thanks: 0 Re: The Equation of a Tangent to a Circle Great. Thank you very much. Tags circle, equation, tangent ### equation of tangent to circle

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