Question 448864
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Hi
Find the equation for the hyperbola with:
vertices at (-1,0),(1,0)(opens right and left) and asymptote of the line y=3x
  x^2/1^2 - y^2/b^2 = 1   Center(0,0) and  a = 1
y = 3x that is b/a = 3  b = 3
 {{{ x^2/1^2 - y^2/9 = 1 }}}
{{{drawing(300,300,  -10,10,-10,10, grid(1), 
circle(-1, 0,0.3),
circle(1, 0,0.3),

graph( 300, 300,-10,10,-10,10,0, 3x, -3x,3sqrt((x)^2-1),-3sqrt((x)^2 -1) ))}}}

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 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.

Using 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)