Question 475404
  <pre><font face = "Tohoma" size = 4 color = "indigo"><b> 
Hi,
What point is the intersection of the graphs: 
x^2 + 4y^2 = 37   
x^2/37 + y^2/9.25 = 1 Ellipse C(0,0) and radius = 5  (See below)
y^2 - x^2 = 8 
y^2/8 - x^2/8 = 1 Hyperbola opening up and down (See below)
y = 3x        Line:  Pt(0,0) and Pt(1,3) on the Line
algebraically:  substituting 3x for y
x^2 + 36x^2 = 37  x = ± 1 and y = ± 3
Graphs: ellipse, hyperbola and Line intersect at:(1,3) and (-1,-3)
{{{drawing(300,300,  -10,10,-10,10,     grid(1), arc(0,0,12.16,6),
circle(1, 3,0.3),
circle(-1, -3,0.3),
graph( 300, 300,-10,10,-10,10,  0,3x,sqrt(x^2+8),-sqrt(x^2+8) ))}}}

Standard Form of an Equation of a Circle is {{{(x-h)^2 + (y-k)^2 = r^2}}} 
where Pt(h,k) is the center and r is the radius

 Standard Form of an Equation of an Ellipse is {{{(x-h)^2/a^2 + (y-k)^2/b^2 = 1 }}}
where Pt(h,k) is the center and a and b  are the respective vertices distances from center.

Standard Form of an Equation of an Hyperbola opening right and  left is:
  {{{(x-h)^2/a^2 - (y-k)^2/b^2 = 1}}} where Pt(h,k) is a center  with vertices 'a' units right and left of center.
Standard Form of an Equation of an Hyperbola opening up and down is:
  {{{(y-k)^2/b^2 - (x-h)^2/a^2 = 1}}} where Pt(h,k) is a center  with vertices 'b' units up and down from center.

The vertex form of a parabola opening up or down, {{{y=a(x-h)^2 +k}}} where(h,k) is the vertex.
The standard form is {{{(x -h)^2 = 4p(y -k)}}}, where  the focus is (h,k + p)

The vertex form of a parabola opening right or left, {{{x=a(y-k)^2 +h}}} where(h,k) is the vertex.
The standard form is {{{(y -k)^2 = 4p(x -h)}}}, where  the focus is (h +p,k )