SOLUTION: I have the following equation: I need to identify the vertices and foci of the hyperbola. I also need to show my work. (y+5)^2/36 - (x+2)^2/25 =1 thank you

 

Hi,

Note: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 and foci  from center along x = h

(y+5)^2/36 - (x+2)^2/25 =1  C(-5,-2) V(,-5,-8) & V(-5,4), F(-5, -2±)

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 and foci {{sqrt(a^2+b^2) from center along y = k.



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 along x = h.



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 )