Thread: intersection of a line and a curve
View Single Post
  #2  
Old July 4th, 2009, 08:51 PM
artvandalay11 artvandalay11 is offline
Owner of The Art of the Proof
  
Join Date: May 2009
Location: New York
Posts: 472
Country:
Thanks: 12
Thanked 169 Times in 162 Posts
artvandalay11 has a spectacular aura aboutartvandalay11 has a spectacular aura about
Default
Quote:
Originally Posted by helloying View Post
Find the coordinates of the points of itersection A and B of the line 2x+y+2=0 and the curve 1/x +2/y= 1/2

i reform the eqn of the line to be y=-2-2x and the curve is \frac{2}{(0.5-1/x)}

then i sub the two eqn and i 2=(0.5-1/x)(-2-2x)

and so x=-2. but i only got one ans and the qn say there are two point of intersection. How to solve this qn?
y=-2-2x, and substitute to get \frac{1}{x}+\frac{2}{-2-2x}=\frac{1}{2}
\frac{1}{x}-\frac{1}{1+x}=\frac{1}{2}

\frac{1+x}{x(1+x)}-\frac{x}{x(1+x)}=\frac{1}{2}

\frac{1}{x+x^2}=\frac{1}{2}

x+x^2=2
x^2+x-2=(x+2)(x-1)=0

x=1 and x=-2 and therefore y=-4 and y=2

so (1,-4) and (-2,2)
__________________

To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.


To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
Reply With Quote
The following users thank artvandalay11 for this useful post:
Donate to MHF