PROBLEMS REQUIRED TO REASSESS
Circle – Write the equation in standard form.
1. 𝑥 2 + 𝑦 2 = 117 − 4𝑥
2. x2 – 2x + y2 + 8y – 8 = 0
3. 4x2 + 4y2 + 36y + 5 = 0
Parabola – Write the equation in standard form
1. Vertex (-1, 2)
Focus (-1,0)
2. Vertex (-2, 1)
Directrix x = 1
Write in standard in standard form and find the vertex, focus, directrix, and sketch the parabola.
3.
𝑥 2 − 2𝑥 + 8𝑦 + 9 = 0
4.
𝑦=
5.
(𝑦 + 2)2 = −16(𝑥 + 3) already in standard form
1
4
𝑥2 +
1
2
𝑥−
7
4
Ellipse - Write the equation in standard form
1. Foci (±5, 0)
Major axis length 12
2. Vertices (0, 4) and (4, 4)
Minor axis length 2
3. Foci (0,0) and (0, 8)
Major axis length 16
4. Center (0, 4) a = 2c Vertices (-4, 4) and (4, 4)
5. 3𝑥 2 + 𝑦 2 + 18𝑥 − 2𝑦 − 8 = 0 sketch ellipse and label vertices, foci, center and endpoints of minor axis
6. 4x2 + 16y2 = 64 sketch ellipse and label vertices, foci, center and endpoints of minor axis
Hyperbola
Sketch and provide center, vertices, foci and equation of asymptotes
1. 9𝑥 2 − 𝑦 2 − 36𝑥 − 6𝑦 + 18 = 0
2. 𝑥 2 − 9 𝑦 2 + 36𝑦 − 72 = 0
Write the equation in standard form
3.
4.
5.
6.
Vertices (0, ±2) Foci (0, ±4)
Vertices (±1, 0) asymptotes 𝑦 = ±5𝑥
Vertices (2, 0) and (6, 0)
Foci (0,0) and (8,0)
Vertices (2, 3) and (2, -3)
Foci (2, 6) and (2, -6)
Write the equation for each graph.
1.
2.
3.
4.