The axis of symmetry of the parabola is the line through this point and the origin,
3x -y = 0
The directrix is the line perpendicular to this through the point that is the reflection of the focus across the vertex. That line can be written as
(x+2) +3(y+6) = 0
x + 3y +20 = 0
The distance from a point (x, y) to a line ax+by+c=0 is given by
d = |ax+by+c|/√(a²+b²)
Of course the distance from a point (x, y) to another point (h, k) is given by the Pythagorean theorem.
d² = (x-h)² +(y-k)²
A parabola is the locus of points equidistant from the focus and the directrix. The squares of those distances will be equal, too. That means our parabola can be described by the equation ...
distance² from (x, y) to focus = distance² from (x, y) to directrix
(x-2)² + (y-6)² = (x +3y +20)²/(1²+3²) . . . . an equation
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Of course, this can be simplified and put in general form, but that does not seem to be a requirement of the problem.
