SOLUTION: Identify the curve and find the center radius and eccentricity? (X+4)^2 + (y+7)^2=81 Please teach me this. I really want to learn how to do it my self. Thank you.

 

Hi

 Circle C(-4,-7) and radius is 9

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 and a and b  are the respective vertices distances from center.



Standard Form of an Equation of an Hyperbola opening right andd 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.



Using 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)