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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 pointslope 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.


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