Question 619017: 1. Identify the focus, directrix, and axis of symmetry of the parabola
a. y= 1/2x^2
b. y^2=16x
2. Identify the vertices, co-vertices and foci of the ellipse
a. x^2/36 + y^2/16 =1
b. (x+5)^2 + y^2/49 = 1
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!
Hi,
a. y= 1/2x^2 Or 2y = x^2 Opening Up: coefficient of x^2 >0
The standard form is  , where the focus is (h,k + p)
V(0,0), F(0,.5) directrix is y = -.5 and axis of symmetry is x= 0
b. y^2 = 16x below...Opening Right: coefficient of y ^2 >0,V(0,0) p = 4
The standard form is  , where the focus is (h +p,k )
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.
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 )
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