SOLUTION: it says, "Write each equation in standard form?" ellipse: 96(x+6)^2 +24(y-4)^2 = 96 hyperbola: 9(x+1)^2 - 16(y+12)^2 =144 parabola: x^2 + 12x + 36 = -8y + 8 i am soo lost!

 

Hi,

Need to know Your Standard forms: See below

 ellipse: 96(x+6)^2 +24(y-4)^2 = 96  ⇒ 

 hyperbola: 9(x+1)^2 - 16(y+12)^2 =144 ⇒ 

 parabola: x^2 + 12x + 36 = -8y + 8  ⇒  

 



 Standard Form of an Equation of an Ellipse is  

where Pt(h,k) is the center. (a variable positioned to correspond with major axis)

 a and b  are the respective vertices distances from center



Standard Form of an Equation of an Hyperbola opening right and  left is:

   with C(h,k) and vertices 'a' units right and left of center,

   

the vertex form of a Parabola opening up(a>0) or down(a<0),  

where(h,k) is the vertex  and  x = h  is the Line of Symmetry

The standard form is , where  the focus is (h,k + p)