Practice Problems

Determine the type of line and sketch them:

Click on the problem number to see the solution.

1. (x-2)^{2} + (y+5)^{2} = 16

2. x^{2} = 20y

3. x^{2}/4 + y^{2} = 1

4. x^{2}/4 – y^{2} = 1

5. x^{2} – 2y^{2} – 2 = 0

6. x^{2} – 2y = 0

7. x^{2} + 2y^{2} – 4 = 0

8. x^{2} – 4x + y = 0

Solutions:

1.

2. x^{2} = 20y PARABOLA: p = 5.

3. x^{2}/4 + y^{2} = 1 ELLIPSE: a = 2, b = 1

4. x^{2}/4 – y^{2} = 1 HYPERBOLA: a = 2, b = 1

5. x^{2} – 2y^{2} – 2 = 0 HYPERBOLA: a = 1.414, b = 1

6. x^{2} – 2y = 0 PARABOLA: p = 1/2

7. x^{2} + 2y^{2} – 4 = 0 ELLIPSE: a = 2, b = 1.414

8. x^{2} – 4x + y = 0 CIRCLE: Center at (2,0). Radius of 2.