My Math Forum  

Go Back   My Math Forum > High School Math Forum > Trigonometry

Trigonometry Trigonometry Math Forum


Reply
 
LinkBack Thread Tools Display Modes
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):
bilano99 is offline  
 
August 30th, 2013, 07:20 AM   #2
Senior Member
 
MarkFL's Avatar
 
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).
MarkFL is offline  
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.
bilano99 is offline  
Reply

  My Math Forum > High School Math Forum > Trigonometry

Tags
circle, equation, tangent



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Arc/Circle Tangent to Circles bmoon Trigonometry 21 August 7th, 2012 08:37 AM
tangent to a circle snigdha Complex Analysis 5 April 17th, 2011 01:12 PM
Tangent to a circle brian890 Trigonometry 3 March 4th, 2011 07:30 PM
Tangent of a circle help? brian890 Trigonometry 1 February 25th, 2011 05:10 PM
Help with circle and tangent point? princediablo Trigonometry 2 May 25th, 2007 09:59 AM





Copyright © 2019 My Math Forum. All rights reserved.