SOLUTION: Please Can you help me !!!!! Write each equation in standard form. State whether the graph of the equation is a parabola, circle,ellipse, or hyperbola. y=x^2+3x+1 Write th

 

Hi,



Write each equation in standard form. State whether the graph of the equation is a parabola, circle,ellipse, or hyperbola.

 y = x^2 + 3x + 1 

y = (x+3/2)^2 -9/4 + 1 = 

y = (x+3/2)^2 -5/4  |Parabola opening upward with Vertex (-3/2,-5/4)

standard form is , (x-3)^2 = y + 5/4



x^2+4y^2+2x-24y+33=0

 (x+1)^2 - 1 + 4(y-3)^2 - 36 + 33 = 0

  (x+1)^2 + 4(y-3)^2 = 4

  (x+1)^2/4 + (y-3)^2 = 1 |Ellipse, C(-1,3) major axis along y = 3





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 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 )