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

_______________________________________________________________________

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 ) 

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