We know that when A = 0 and B and C are nonzero values, the equation By2 + Cx + Dy + F = 0 represents a parabola that opens left or right. |
As with the equation Ax2 + Cx + Dy + F = 0, which we studied earlier, the equation By2 + Cx + Dy + F = 0 does not provide us with enough information to easily draw a graph of a parabola. |
Remember that we used a method called completing the square to rewrite the equation Ax2 + Cx + Dy + F = 0 into standard form for parabolas that open up or down: y - k = a(x - h)2. |
Similarly, we use this method again to rewrite the equation By2 + Cx + Dy + F = 0 into the standard form for parabolas that open left or right, x - h = a(y - k)2. |
As before, the coordinates (h, k) denote the vertex of the parabola, and a descibes the shape and direction of the parabola. |
Using the same steps as before, let's look at a few examples to see how this is done. |