November 11th, 2016, 06:39 PM  #1 
Senior Member Joined: Nov 2010 From: Indonesia Posts: 1,767 Thanks: 121 Math Focus: Trigonometry and Logarithm  [ASK] About Circles in Coordinates
3. A(a,b), B(a,b), and C is plane XOY. P moves along with curve C. If the multiplication product of PA's and PB's gradients are always k, C is a circle only if k = ...? 4. The radius of a circle which meets Xaxis at (6,0) and meets the curve $\displaystyle y=\sqrt{3x}$ at one point is .... 5. A circle meets the line x + y = 3 at (2,1). It also meets the point (6,3). Its radius is .... I have no idea how to do number 3, or even the meaning. For number 4, I substituted x = 6 and y = 0 to the equation $\displaystyle (xa)^2+(yb)^2=r^2$ and got $\displaystyle 3612a+a^2+b^2=36$. For number 5, I substituted both coordinates to the circle equation and got 2a + b = 10. Please help how to continue each number. 
November 12th, 2016, 01:43 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,586 Thanks: 1489 
3. If P is the point (x, y), PA and PB have gradients (y  b)/(x  a) and (y + b)/(x + a) respectively. If the product of those gradients is k, (y²  b²)/(x²  a²) = k, and so kx² + y² = ka² + b². Can you finish from there? Note that PA and PB needn't both have gradients. 

Tags 
circles, coordinates 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
How do you show a Möbius transformation maps circles to circles and lines?  math93  Geometry  0  November 3rd, 2015 03:43 PM 
RiDo Circles. Sin & Cos Circles  RiDo  Algebra  2  June 21st, 2012 02:31 AM 
Converting cartesian coordinates to polar coordinates  Eppo  Algebra  5  January 9th, 2008 02:35 PM 
Cartesian coordinates to oblique coordinates  dex2l  Algebra  4  November 2nd, 2007 05:30 AM 
Cartesian coordinates to spherical coordinates  blazingclaymore  Computer Science  4  July 18th, 2007 06:59 PM 