Question 614074
  <pre><font face = "Tohoma" size = 3 color = "indigo"><b> 
Hi, 
{{{(x-3)^2/64 + (y + 5)^2/100 = 1}}} 
{{{(x-3)^2/8^2 + (y + 5)^2/10^2 = 1}}} 
Vertical ellipse C(3,-5), major = 20 and minor = 16
{{{drawing(300,300,    -8,12,-15,8,   arc(3,-5,16,20),
 grid(1),
circle(3, -5,0.4),
graph( 300, 300, -8,12,-15,8))}}}
{{{y^2/5^2 - (x-6)^2/12^2 = 1}}} Hyperbola opening Up and down
C(6,0) V(6,5)&(6,-5) Major Axis is 10 and Minor is 24
Asymptotes: m = ±5/12, y = mx + b Using Pt(6,0)to solve for b, {{{y = (5/12)x-5/2}}}  and {{{y = (-5/12)x + 5/2}}}
{{{drawing(300,300, -20,20,-20,20,blue(line(6,20,6,-20))   
 grid(1),
circle(6, 5,0.4),
circle(6, -5,0.4),
graph( 300, 300, -20,20,-20,20,0, (5/12)x - 5/2,-(5/12)x + 5/2, 5sqrt(1+(x-6)^2/144),-5sqrt(1+(x-6)^2/144)  ))}}}