Pre Calc
posted by Asher on .
Derive the equation of the locus of all points that are equidistant from the point F(3,4) and the line y=2. Leave your answer in general form. [General Form: ax^2+by^2+cx+dy+e=0]

It will be a parabola. The vertical axis will be at x = 3. F is the focal point. The vertex of the parabola is equidistant from F and the y = 2 line, at x = 3, y = 1.
y = a (x+3)^2 + 1 is the equation.
Do some reading up on parabolas to figure out what a is. I think you will find it is 4 times the distance from the focus to the vertex, or 4*3 = 12
That would make the equation
y = 12(x+3)^2 + 1
Expand and rearrange that to the "general form".