Question 851770
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Hi,
1. circle with center at (3,-1) and radius is 4 {{{(x-3)^2 + (y+1)^2 = 4^2 }}} 
2. Ellipse with vertex at(0,12) and co-vertices at(-8,0), C(0,0) {{{(x)^2/12^2 + (y)^2/8^2 = 1 }}} 
3. Hyperbola with vertex at (0,4),focus at(0,5) and center at(0,1)
{{{(y-1)^2/3^2 - (x)^2/7 = 1}}} 4 = sqrt(3^2 + 7 )
Standard Form of an Equation of an Hyperbola opening up and down is:
  {{{(y-k)^2/b^2 - (x-h)^2/a^2 = 1}}} with C(h,k) and vertices 'b' units up and down from center,  
Foci {{{sqrt(a^2+b^2)}}}units units up and down from center, along x = h