Parabola Problems

1Determine the equations of the following parabolas and indicate the values of their focal parameter, focus and directrix.

1 Parabola Problem

2 Parabola Problem

2Determine the equations of the parabolas using the information given:

1 The directrix is x = −3 and the focus is (3, 0).

2 The directrix is y = 4 and the focus is (0, 0).

3 The directrix is y = −5 and the focus is (0, 5).

4 The directrix is x = 2 and the focus is (−2, 0).

5 The focus is (2, 0) and the vertex is (0, 0).

6 The focus is (3, 2) and the vertex is (5, 2).

7 The focus is (−2, 5) and the vertex is (−2, 2).

8 The focus is (3, 4) and the vertex is (1, 4).

3Calculate the vertex, focus and directrix of the following parabolas:

1 Parabola Problem

2 Parabola Problem

3 Parabola Problem

4Find the equation of the vertical parabola that passes through the points: A = (6, 1), B = (−2, 3) and C = (16, 6).

5Determine the equation of the parabola with a directrix of y = 0 and a focus at (2, 4).

6Determine the point(s) of intersection between the line r ≡ x + y − 5 = 0 and the parabola y2 = 16x.

7Find the equation of the horizontal parabola that passes through the point (3, 4) and has its vertex at (0, 0).

8Determine the equation of the parabola with an axis parallel to the y-axis, vertex on the x-axis and which passes through the points A = (2, 3) and B = (−1, 12).

9Determine the equation of the parabola with a directrix of x + y − 6 = 0 and a focus at (0, 0).

 

1

Determine the equations of the following parabolas and indicate the values of their focal parameter, focus and directrix.

1 Parabola Exercise

Horizontal Parabola

Parabola Calculations

Parabola Calculations

Parabola Solution

 

2 Parabola Exercise

Horizontal Parabola

Parabola Calculations

Parabola Calculations

Parabola Solution

 

3 Parabola Exercise

Vertical Parabola

Parabola Calculations

Parabola Calculations

Parabola Solution

 

2

Determine the equations of the parabolas using the information given:

1 The directrix is x = −3 and the focus is (3, 0).

Horizontal Parabola

Parabola Calculations

Parabola Solution

 

2 The directrix is y = 4 and the focus is (0, 0).

 

Vertical Parabola

Parabola Calculations

Parabola Solution

 

3 The directrix is y = −5 and the focus is (0, 5).

Vertical Parabola

Parabola Calculations

Parabola Solution

 

4 The directrix is x = 2 and the focus is (−2, 0).

Horizontal Parabola

Parabola Calculations

Parabola Solution

 

5 The focus is (2, 0) and the vertex is (0, 0).

Horizontal Parabola

Parabola Calculations

Parabola Solution

 

6 The focus is (3, 2) and the vertex is (5, 2).

Horizontal Parabola

Parabola Calculations

Parabola Solution

 

7 The focus is (−2, 5) and the vertex is (−2, 2).

Vertical Parabola

Parabola Calculations

Parabola Solution

 

8 The focus is (3, 4) and the vertex is (1, 4).

Horizontal Parabola

Parabola Calculations

Parabola Solution

 

3

Calculate the vertex, focus and directrix of the following parabolas:

1 Parabola Exercise

Horizontal Parabola

Parabola Calculations

Parabola Calculations

Parabola Calculations

Parabola Calculations

Parabola Calculations

Parabola Solution

 

2 Parabola Exercise

Vertical Parabola

Parabola Operations

Parabola Operations

Parabola Operations

Parabola Operations

Parabola Operations

Parabola Solution

 

3 Parabola Exercise

Vertical Parabola

Parabola Operations

Parabola Operations

Parabola Operations

Parabola Operations

Parabola Operations

Parabola Solution

 

4

Find the equation of the vertical parabola that passes through the points: A = (6, 1), B = (−2, 3) and C = (16, 6).

Parabola Operations

Parabola Operations

Parabola Operations

Parabola Solution

 

5

Determine the equation of the parabola with a directrix of y = 0 and a focus at (2, 4).

Parabola Operations

Parabola Operations

Parabola Operations

Parabola Solution

 

6

Determine the point(s) of intersection between the line r ≡ x + y − 5 = 0 and the parabola y2 = 16x.

Points of Intersection

Parabola Operations

Parabola Operations

Parabola Operations

Parabola Solution

 

7

Find the equation of the horizontal parabola that passes through the point (3, 4) and has its vertex at (0, 0).

Parabola Operations

Parabola Solution

 

8

Determine the equation of the parabola with an axis parallel to the y-axis, vertex on the x-axis and which passes through the points A = (2, 3) and B = (−1, 12).

Parabola Operations

Parabola Operations

Parabola Operations

Parabola Operations

Parabola Solution

 

9

Determine the equation of the parabola with a directrix of x + y − 6 = 0 and a focus at (0, 0).

Parabola Operations

Parabola Operations

Parabola Solution

 



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