SOLUTION: it says, "Identify the curve and find the characteristics listed. then sketch the curve." (x-3)^2/9 + (y+3)^2/16= 1 center vertices foci y^2/16 - x^2/9 = 1 center asymptotes

 

Hi,  Standard Forms are the quidelines

Standard Form of an Equation of an Ellipse is  

where Pt(h,k) is the center. (a variable positioned to correspond with major axis)

 a and b  are the respective vertices distances from center

 and ±are the foci distances from center: a > b

(x-3)^2/9 + (y+3)^2/16= 1 C(3,-3), V(0,-3)& V(6,-3), V(3,1) &(3,-7), 

F(3, -3 + sqrt(7)) and F(3,-3-sqrt(7))







Standard Form of an Equation of an Hyperbola opening up and down is:

   with C(h,k) and vertices 'b' units up and down from center,  2b the length of the transverse axis

Foci units units up and down from center, along x = h

& Asymptotes Lines passing thru C(h,k), with slopes m =  ± b/a