Hi
-x^2 + y^2 - 6x -10y +17=0
x^2 - y^2 + 6x +10y -17=0 ||multiplying thru by -1
(x+3)^2 -9 -(y-5)^2+25-17=0
|Note: C(-3,5) a=1 and b = 1
Note:
Standard Form of an Equation of an Hyperbola opening right and left is:
where Pt(h,k) is a center with vertices 'a' units right and left of center.
a.find the vertices: with Center(-3,5)and a=1..V(-4,5) and V(-2,5)
b.find the length of the focal radius 
c.find the slopes of the asymptotes m = ±b/a = ± 
d.find the length of the conjugate axis: 2b is the conjugate axis length = 
See below descriptions of various conics
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Standard Form of an Equation of a Circle is 
where Pt(h,k) is the center and r is the radius
Standard Form of an Equation of an Ellipse is 
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 ±
are the foci distances from center: a > b
Standard Form of an Equation of an Hyperbola opening right and left is:
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:
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, 
where(h,k) is the vertex.
The standard form is 
, where the focus is (h,k + p)
the vertex form of a parabola opening right or left, 
where(h,k) is the vertex.
The standard form is 
, where the focus is (h +p,k )
