Pre Calc

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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]

• Pre Calc -

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".

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