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Hotmath
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Hotmath
Chapter: Quadratic Relations/Analytic Geometry Section: Hyperbolas
 

Problem: 1

Rewrite the equation of the hyperbola in standard form.

16 x 2 – 4 y 2 = 64

 

Problem: 3

Rewrite the equation of the hyperbola in the standard form.

100 y 2 – 9 x 2 = 25

 

Problem: 5

Rewrite the equation of the hyperbola in standard form.

y 2 – 9 x 2 = 36

 

Problem: 7

Calculate the vertices and foci of the hyperbola.

 

Problem: 9

Determine the vertices and foci of the hyperbola:

 

Problem: 11

Rewrite the equation in standard form. Determine the foci and vertices.

4 x 2 – 25 y 2 = 100

 

Problem: 13

Rewrite the equation in standard form. Identify the vertices and foci of the hyperbola.

49 y 2 – 16 x 2 = 784

 

Problem: 15

Graph the equation and identify the foci and asymptotes:

 

Problem: 17

Graph the equation and identify the foci and asymptotes:

 

Problem: 19

Graph the equation 100 x 2 – 64 y 2 = 6400 and identify the foci and asymptotes.

 

Problem: 21

Graph the equation: x 2 + y 2 = 20

 

Problem: 23

Graph the equation: x 2 = 25 y

 

Problem: 25

Graph the hyperbola:

 

Problem: 27

Graph the inequality y 2 x 2 9

 

Problem: 29

Graph the inequality

 

Problem: 31

Find an equation of the hyperbola with the given foci and vertices.

Foci: (–10, 0), (10, 0), Vertices: (–9, 0), (9, 0)

 

Problem: 33

Find an equation of the hyperbola with the given foci and vertices.

Foci: (0, –16), (0, 16), Vertices: (0, –7), (0, 7)

 

Problem: 35

Write an equation of the parabola, given:

Center: (0, 0)

Foci: (–5, 0), (5, 0)

Vertices: (–2, 0), (2, 0)

 

Problem: 37

An equation for a hyperbola is given. Obtain two points on the curve with x –coordinate equal to 4.

 

Problem: 39

Find the asymptotes of the parabola:

Sketch its graph.

 

Problem: 41

Determine the foci of the hyperbola whose:

Vertices: (–2, 0), (2, 0)

Asymptotes: y = 5 x , y = –5 x

 

Problem: 43

A hyperbola with endpoints of the transverse axis at (–3, 0) and (3, 0) is centered at the origin. The square of the distance from the center to a focus is 45. Find an equation and graph the hyperbola.

 

Problem: 45

Identify the common features of the given hyperbolas.

And also identify in what way does the given hyperbolas differ .

 

Problem: 47

The coordinates of foci and the difference of focal radii are given. Use the definition of hyperbola and find the equation.

Foci: (–4, 0) and (4, 0)

Difference of focal radii = 4