SOLUTION: write an equation for a graph that is the set of all points in the plane that are equidistant from the given point and the given line. F(0,2) y= -2

 

Hi

write an equation for a graph that is the set of all points in the plane that

 are equidistant from the given point(0,2) and y = -2

Parabola opening upward:  C(0,0)

 4py = x^2    p = 2 

  8y = x^2   or y = x^2/8





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 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)