Hi,

Converting each equation to the standard form of conic section

y^2+6y-x=0   |Parabola opening right or left

 x = y^2+6y

 x = (y+3)^2 - 9   |Vertex form V(-9,-3)

 

x^2-y^2-6x+13=0  |Hyperbola opening up and down (multiplying thru by -1)

 y^2 - x^2 + 6x -13 = 0

 y^2 -[(x-3)^2 -9] - 13 = 0

 y^2 -(x-3)^2 +9 - 13 = 0

 y^2 - (x-3)^2 = 4 





 

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