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Conic Sections

Problems

Parabolas

Ellipses and Circles

Problem : Find the vertex, focus, axis, and directrix of the following parabola: x 2 - 4x - 8y + 28 = 0 .

Vertex: (2, 3) . Focus: (2, 5) . Axis: x = 2 . Directrix: y = 1 .

Problem : Find the vertex, focus, axis, and directrix of the following parabola: y 2 + 4x - 2y - 3 = 0 .

Vertex: (1, 1) . Focus: (0, 1) . Axis: y = 1 . Directrix: x = 2 .

Problem : Find the vertex, focus, axis, and directrix of the following parabola: x 2 - 4y = 0 .

Vertex: (0, 0) . Focus: (0, 1) . Axis: x = 0 . Directrix: y = - 1 .

Problem : Find the vertex, focus, axis, and directrix of the following parabola: x 2 - 10x - 2y + 29 = 0 .

Vertex: (5, 2) . Focus: (5, 2.5) . Axis: x = 5 . Directrix: y = 1.5 .

Problem : Find the vertex, focus, axis, and directrix of the following parabola: y 2 - 16x + 16 = 0 .

Vertex: (0, 1) . Focus: (4, 1) . Axis: y = 1 . Directrix: x = - 4 .

Problem : Find the vertex, focus, axis, and directrix of the following parabola: y = x 2 + 3x + 6 .

Vertex: (- ,) . Focus: (- , 4) . Axis: x = - . Directrix: y = .

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