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July 5th, 2009, 04:50 PM  #1 
Member Joined: Jul 2009 Posts: 40 Thanks: 0  Write the equation of the tangent line by (2,2√2)
I already graphed x^26x+y^2=0, which gave me a circle , but how in the world should I write an equation? I think it might be a linear equation. Any step on how to solve? Thanks in advance.
Last edited by skipjack; February 28th, 2018 at 01:34 PM. 
July 5th, 2009, 05:20 PM  #2 
Senior Member Joined: May 2008 From: Sacramento, California Posts: 299 Thanks: 0  re: Write the equation of the tangent line by (2,2√2)
I'm assuming you know calculus. Use implict differentiation to find the derivative of the equation: $\displaystyle 2x6+2y\frac{dy}{dx}=0$ $\displaystyle 2y\frac{dy}{dx}=2x+6$ $\displaystyle \frac{dy}{dx}=\frac{x+3}{y}$ Then find the slope of the tangent line at (2, 2√2): $\displaystyle \frac{x+3}{y}$ $\displaystyle \frac{1}{2\sqrt{2}}$ You can find the equation of the tangent line by using pointslope form: $\displaystyle \frac{1}{2\sqrt{2}}(x2)+2\sqrt{2}$ So the equation of the tangent line is $\displaystyle \frac{1}{2\sqrt{2}}(x2)+2\sqrt{2}$. Last edited by skipjack; February 28th, 2018 at 01:39 PM. 
July 5th, 2009, 06:07 PM  #3  
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0  re: Write the equation of the tangent line by (2,2√2) Quote:
Last edited by skipjack; February 28th, 2018 at 01:37 PM.  
July 5th, 2009, 06:11 PM  #4 
Member Joined: Jul 2009 Posts: 40 Thanks: 0  re: Write the equation of the tangent line by (2,2√2)
Thank you so much and by the way no I have not taken Calculus yet; that is why I had no idea on solving my question. Thank you very much.
Last edited by skipjack; February 28th, 2018 at 01:31 PM. 
July 5th, 2009, 06:40 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,941 Thanks: 2210 
Given the point (x_0, y_0) on the circle with equation $\displaystyle (x\,\,a)^{\small2}\,+\,(y\,\,b)^{\small2}\,=\,r^{\small2},$ the tangent through that point has equation $\displaystyle (x_0\,\,a)(xa)\,+\,(y_0\,\,b)(y\,\,b)\,=\,r^{\small2},$ which is easy to remember.
Last edited by skipjack; February 28th, 2018 at 01:31 PM. 
July 5th, 2009, 06:43 PM  #6 
Member Joined: Jul 2009 Posts: 40 Thanks: 0  re: Write the equation of the tangent line by (2,2√2)
hmmm good point, that is easier. Also, to write an equation to the circle symmetric about the x axis to the line. Would it be this? 1/2√2(x2)2√2. It seems right to be since the original tangent line is 1/2√2(x2)+2√2. Last edited by skipjack; February 28th, 2018 at 01:36 PM. 
July 6th, 2009, 03:31 AM  #7 
Global Moderator Joined: Dec 2006 Posts: 20,941 Thanks: 2210 
No. To reflect any function in the xaxis, just negate the entire function (i.e., the graph of y = f(x) is the reflection in the xaxis of the graph of y = f(x)). By the way, you should write your final answers as equations, as requested in the question. 

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