Parabola
If and are, respectively, the vertex and focus of the parabola , find .
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1 solution
Putting this parabola into standard form:
y^2 + 6y + 2x + 5 = 0;
or y^2 + 6y + 9 - 4 + 2x = 0;
or (y+3)^2 = -2x + 4;
or (y+3)^2 = -2*(x-2).
which is a concave-left parabola. Hence, the vertex is V(2, -3), and 4p = -2 => p = -1/2. This puts the focus at S(3/2, -3). The length of SV is just 2 - 3/2 = 1/2 = 0.5.