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foci 3x2+2x+5y−6=0
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Solution
(−13,1720)
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Parabola Focus
A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (the directrix)
Parabola standard equation
4p(y−k)=(x−h)2 is the standard equation for an up-down facing parabola with vertex at (h,k), and a focal length |p|
Rewrite 3x2+2x+5y−6=0in the standard form
4(−512)(y−1915)=(x−(−13))2
(h,k)=(−13,1915),p=−512
Parabola is symmetric around the y-axis and so the focus lies a distance p from the center (−13,1915) along the y-axis