October 28th, 2011, 06:39 AM  #1 
Newbie Joined: Oct 2011 Posts: 2 Thanks: 0  Circle Geometry
I have 3 questions which I'm unsure how to do (or have some idea but not entirely sure of all parts) on circle geometry. Help on any of these questions would be wonderful. 6) A circle passes through the points Q(0,3) and R (0,9) and touches the x axis. Work out two possible equations. Now for this I know that you need to first find the coordinate for where the circle touches the x axis and I will most likely know what to do from there. But I'm not sure how to go about doing this :/ 7) i) Show that the line y= 4x is a tangent to the circle x^2 + y^2 = 8 ii) Show that the line 4y= 3x25 is a tangent to the circle x^2+y^2 = 25 I know what a tangent is, I just don't know how you go about showing it? Find the coordinates of the point where the following lines and parabolas intersect. i) y = 3x+ 1 and y = x^2  4x +7 ii) y = x 2 and y = x^2 + 2x8 I have never heard of the word parabola in my life! 
October 28th, 2011, 07:54 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,635 Thanks: 2080 
6) Let S(x, y) be the centre of the circle, then it touches the xaxis at (x, 0). Can you see why y = 6? How far is S from Q and R? 7) Consider where the line and circle intersect. For a tangent, there is exactly one such point. 8) This requires solving simultaneous equations. I recommend you eliminate y and then solve for x. 
October 28th, 2011, 08:26 AM  #3 
Newbie Joined: Oct 2011 Posts: 2 Thanks: 0  Re: Circle Geometry
6) Yes I think I understand why y is 6, but how do I solve for x? 7) And how would I go about this? 8) That seems simple enough, I can do that, thank you 
October 28th, 2011, 04:08 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,635 Thanks: 2080 
6) You didn't answer my second question. 7) Where the graphs intersect, the coordinates satisfy both equations, so you can proceed as described for question 8, and hence find out how many solutions there are. 
October 30th, 2011, 12:49 AM  #5 
Senior Member Joined: Oct 2011 From: India ???? Posts: 224 Thanks: 0  Re: Circle Geometry
Q 6) Let the equation of the circle be . Since (0,3) and(0,9) lie on the circle: and Subtracting: ___________________________ Since xaxis touches the circle: In the equation of circle: Therefore the centers of the circles are and and the . Q7) The line is tangent to the curve if it touches it at only 1 point. Substituting y in equation of the curve: Only 1 solution exists. The line is tangent to the curve. Q(i) and . Solving these two by substitution. Therefore . So the line intersects the parabola at and . (ii) Do the same as in (i). 
October 30th, 2011, 04:55 AM  #6  
Global Moderator Joined: Dec 2006 Posts: 20,635 Thanks: 2080  Quote:
As the distance of (x, 6) from Q(0, 3) is 6, x² + 9 = 36, and so x = ±3?3. Hence the equations of the possible circles are (x ± 3?3)² + (y  6)² = 36.  

Tags 
circle, geometry 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Circle Geometry  AzraaBux  Geometry  1  May 30th, 2013 02:42 PM 
geometry  circle  sy14427  Geometry  3  April 27th, 2013 09:38 AM 
GeometryCircle  winner  Geometry  1  January 13th, 2011 10:27 PM 
Geometry Circle problem  iaahs  Geometry  1  February 3rd, 2008 04:31 PM 
Circle Geometry  symmetry  Geometry  2  February 19th, 2007 04:47 PM 