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 )