# The graph of y=x+1/x is shown on the insert. The lowest point on the branch is (1,2)

• Jan 8th 2011, 11:06 AM
moesizlak
The graph of y=x+1/x is shown on the insert. The lowest point on the branch is (1,2)
...The highest point on the other branch is(-1,-2)
(i) Use the graph to solve the following equations, showing your method clearly
A x+1/x=4
B 2x+1/x=4
The equation (x-1)^2 +y^2=4 represents a circle. Find in exact form the coordinates of the points of intersection of this circle with the y-axis

i) State the radius and the coordinates of the centre of this circle.
Explain how these can be used to deduce from the graph that this circle touches one branch
of the curve y=x+1/x but does not intersect with the other
My test is on monday need help thorugh past papers pleaseeee thanks in advance
• Jan 8th 2011, 11:42 AM
Quote:

Originally Posted by moesizlak
...The highest point on the other branch is(-1,-2)
(i) Use the graph to solve the following equations, showing your method clearly
A x+1/x=4
B 2x+1/x=4
The equation (x-1)^2 +y^2=4 represents a circle. Find in exact form the coordinates of the points of intersection of this circle with the y-axis

i) State the radius and the coordinates of the centre of this circle.
Explain how these can be used to deduce from the graph that this circle touches one branch
of the curve y=x+1/x but does not intersect with the other
My test is on monday need help thorugh past papers pleaseeee thanks in advance

A.

$y=4$ is a horizontal line 4 units above the x-axis.

This line intersects $x+\frac{1}{x}$ directly above the value of x required on the x-axis.

B.

$2x+\frac{1}{x}=4\Rightarrow\ x+\frac{1}{x}=4-x$

Draw a line with slope $-1$ cutting the y-axis at $(0,\;4)$

The intersection of this line with $x+\frac{1}{x}$ gives the solutions
(directly below the points of intersection on the x-axis).