the graphs of the equations xy=16 and y=x are drawn on the same set of axes. In which quadrant or quadrants will they intersect?
Given the curves:
Then we will rewrite as a function of x.
==> y= 16/x ...........(1)
And the curve :
We need to find the intersections points .
==> y= y
==> x = 16/x
We will multiply by x.
==> x^2 = 16
==> x = +-4
Then, we have two intersection points at x1= 4 and x2= -4
Now we will find the y-coordinate.
==> y1= x1= 4
==> y2= x2= -4
Then, the points of intersection are :
(4,4) and (-4,-4)
The point (4,4) is located in the first quadrant and the point (-4,-4) is located in the third quadrant.