Sketch the Graph of x^2=y^2=9

2 answers

x^2=y^2=9
x^2 - y^2=9

x^2 /9 - y^2 / 9 = 1

You have a hyperbola with centre (0,0) and a=3, and b=3

vertices are (3,0) and (-3,0)

draw a square with sides 6 and centre it at the origin
draw the diagonals of this square and extend them in all four directions.
These two extended diagonal are the asymptotes of your hyperbola

Sketch your two parts of the hyperbola with centres given above and approaching these asymptotes
Find the equation of a hyperbola which is generated by a point that moves so that the difference of its distance from the points (-4,1) and (2,1) is 4.