Question 475401
  <pre><font face = "Tohoma" size = 4 color = "indigo"><b> 
Hi,
What point is the intersection of the graphs: 
x^2 + y^2 = 34   circle C(0,0) and radius = sqrt(34) 
x^2 -4y = 13 OR y = .25x^2 - 13/4  Parabola opening upward V(0,-3.25)
algebraically:  substituting (13+4y) for x^2
13+4y + y^2 = 34
  y^2 + 4y -21 = (y + 7)(y-3)  |tossing out y = -7 as Extraneous
y = 3 then x^2 = 25 , x = ± 5
Graphs: parbola and circle intersect at:( 5,3) and (-5,3)
{{{drawing(300,300,   -6, 6, -6, 6,   grid(1),
circle(0, 0,0.3),
circle(0, 0,5.83),
circle(0, -3.25,0.3),
circle(5, 3,0.3),
circle(-5, 3,0.3),
graph( 300, 300, -6, 6, -6, 6,0,.25x^2 - 13/4 ))}}}


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 )