What are the four corners of the fundamental rectangle of the hyperbola (-x^2/36)+(y^2/49)=1?

Answer 1

(-(x^2)/36) + ((y^2)/49) = 1

-(((x^2)/36) - ((y^2)/49)) = 1

((x^2)/36) - ((y^2)/49) = -1

ANS : (6i,0), (-6i,0), (0,7), and (0,-7)

Answer 2

The positive term in left side indicate that the vertexes are on y axes
So, the vertexes are the points (0,7) and (0,-7)
The other two points you get from the other term and they are on x axes... (6,0) and (-6,0)

Now you plot the rectangle and trace the diagonal lines that are the asymptotes of the hyperbola.

The graphic is external to the rectangle and go through the vertexes.