Question 608618
  <pre><font face = "Tohoma Ital" size = 3 color = "indigo"><b> 
Hi
Classify the conic section, write it's equation in standard form, and graph.
y^2-2y-4x-7=0
(y-1)^2-1 - 4x-7 = (y-1)^2-4x-8 = 0  OR  (1/4)(y-1)^2 -2 =x
{{{ x = (1/4)(y-1)^2 -2 }}}
Note:
the vertex form of a parabola opening right or left, {{{x=a(y-k)^2 +h}}} where(h,k) is the vertex.  V(-2,1)
The standard form is {{{(y -k)^2 = 4p(x -h)}}}, where  the focus is (h +p,k) {{{(y-1)^2 = 4(x+2)}}}
{{{drawing(300,300,   -10,10,-10,10,  
 grid(1),
graph( 300, 300, -10,10,-10,10,0,1 + sqrt(4x +8),1 - sqrt(4x +8)))}}} 

See below descriptions of various conics
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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. (a positioned to correspond with major axis)
 a and b  are the respective vertices distances from center and ±{{{sqrt(a^2-b^2)}}}are the foci distances from center: a > b

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 )