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Chapter: Quadratic Relations/Analytic Geometry Section: Parabolas
 

Problem: 1

The coordinates of vertex of a parabola are V (3, 2) and equation of directrix is y = –2. Find the coordinates of focus.

 

Problem: 3

The coordinates of focus and vertex of a parabola are F (2, –2) and V (2, –5) respectively. Find the equation of directrix.

 

Problem: 5

Find the direction in which the parabola with vertex at (1,1) and focus (1,4) open.

 

Problem: 7

Find an equation of parabola with focus (0, 0) and directrix y = 6, also graph it.

 

Problem: 9

Find an equation of parabola with focus (0, 4) and directrix x = 4, also graph it.

 

Problem: 11

Sketch the parabola:

y 2 = 8 x

 

Problem: 13

Sketch the parabola:

x 2 = 4 y

 

Problem: 15

Determine whether the parabola has a vertical or horizontal axis.

y = –5 x 2

 

Problem: 17

Determine whether the parabola has a vertical or horizontal axis.

2 y 2 = 5 x

 

Problem: 19

Decide whether the parabola opens up, down, left, or right.

 

Problem: 21

Decide whether the parabola opens up, down, left, or right.

–7 x 2 = 4 y

 

Problem: 23

Decide whether the parabola opens up, down, left, or right.

9 y 2 = x

 

Problem: 25

Tell whether the parabola opens up, down, left, or right.

2 y 2 = – 6 x

 

Problem: 27

Does the parabola open left, right, up, or down?

 

Problem: 29

Does the parabola x 2 + 16 y = 0 open left, right, up, or down?

 

Problem: 31

Find the focus and directrix of the parabola.

3 y 2 = x

 

Problem: 33

Find the focus and directrix of the parabola.

x 2 = –24 y

 

Problem: 35

Graph the equation and then find the focus and directrix of the parabola.

x 2 = –5 y

 

Problem: 37

Graph the equation and then find the focus and directrix of the parabola.

y 2 = 16 x

 

Problem: 39

Graph the equation and then find the focus and directrix of the parabola.

 

Problem: 41

Identify the focus and directrix, and then graph the parabola:

 

Problem: 43

Identify the focus and directrix, and then graph the parabola:

x 2 = –6 y

 

Problem: 45

Give the standard form of the equation of the parabola with given focus (–1, 0) and vertex at (0, 0).

 

Problem: 47

Give the standard form of the equation of the parabola with given focus (0, –5/8) and vertex at (0, 0).

 

Problem: 49

Give the standard form of the equation of the parabola with given directrix

y = –5 and vertex at (0, 0).

 

Problem: 51

Give the standard form of the equation of the parabola with given directrix x = 8 and vertex at (0, 0).

 

Problem: 53

Find the equation of a parabola with directrix y = 10 and vertex at the origin.

 

Problem: 55

Find the equation of a parabola with focus at (0, –8) and vertex at the origin.

 

Problem: 57

Find whether the given equation is a parabola or a circle and then graph the equation.

7 x 2 + 7 y 2 = 252

 

Problem: 59

Find an equation of parabola with focus (2, 4) and vertex (2, 2), and graph it.

 

Problem: 61

Find the vertex, focus, directrix, and axis of symmetry of the parabola:

x 2 + 4 y + 2 x –3 = 0

 

Problem: 63

Find the vertex, focus, directrix, and axis of symmetry of the parabola:

y 2 – 4 y – 4 x + 2 = 0