Exercise 1

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

1

2

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Exercise 2

Determine 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 vertex 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).

Exercise 3

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

1

2

3

Exercise 4

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

Exercise 5

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

Exercise 6

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

Exercise 7

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

Exercise 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).

Exercise 9

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

Solution of exercise 1

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

1

 

2

 

3

 

Solution of exercise 2

Determine 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 vertex 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).

 

Solution of exercise 3

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

1

 

2

 

3

 

Solution of exercise 4

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

 

Solution of exercise 5

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

 

Solution of exercise 6

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

 

Solution of exercise 7

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

 

Solution of exercise 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).

 

Solution of exercise 9

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

 

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.

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