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Write equations of hyperbolas in standard form using properties

Write the standard form equation for a hyperbola with center at the origin, vertices at

(0,6)

(0,-6)

(0,9)

(0,-9)

A triangle has side lengths of

(10 w+9)

(5 w-3)

centimeters, and

(8 x+10)

centimeters. Which expression represents the perimeter, in centimeters, of the triangle?

\newline

21 w+18 x

\newline

8 x+15 w+16

\newline

18 x+6+15 w

\newline

18 x+19 w+2

A triangle has vertices on a coordinate grid at

F(1,-1), G(1,3)

H(-8,-1)

. What is the length, in units, of

\overline{F G}

\newline

\square

A triangle has vertices on a coordinate grid at

S(-1,7), T(-1,-1)

U(-5,7)

. What is the length, in units, of

\overline{S T}

\newline

\square

A triangle has vertices on a coordinate grid at

F(3,-2), G(3,9)

H(-6,-2)

. What is the length, in units, of

\overline{F G}

\newline

\square

A triangle has vertices on a coordinate grid at

A(3,-6), B(-6,-6)

C(-6,-1)

. What is the length, in units, of

\overline{A B}

\newline

\square

A triangle has vertices on a coordinate grid at

E(-9,-10), F(-9,9)

G(8,9)

. What is the length, in units, of

\overline{E F}

\newline

\square

6

. Find the equation of the hyperbola with the vertices

(0,3)(10,3)

and the asymptotes

y=2 / 5 x+1

y=-2 / 5 x+5

A rectangle is shown on the coordinate grid with vertices

(-3,0),(-1,0),(-3,3)

(-1,3)

. A solid is formed by rotating the rectangle about the line

x=-1

\newline

Select all true statements about the revolved solid.

\newline

The revolved solid is a cylinder with a base radius of

2

\newline

The revolved solid is a cylinder with a base radius of

1

\newline

The revolved solid is a cylinder with a height of

2

\newline

The revolved solid is a cylinder with a height of

3

\newline

The revolved solid is a rectangular prism with a base length of

2

\newline

The revolved solid is a rectangular prism with a base length of

4

\newline

37241931

42870

A rectangle is shown on the coordinate grid with vertices

(-4,0),(0,0),(0,2)

(-4,2)

. A solid is formed by rotating the rectangle about the

x

\newline

Select all true statements about the revolved solid.

\newline

The revolved solid is a cylinder with a base radius of

2

\newline

The revolved solid is a cylinder with a base radius of

4

\newline

The revolved solid is a cylinder with a height of

2

\newline

The revolved solid is a cylinder with a height of

4

\newline

The revolved solid is a rectangular prism with a base length of

2

\newline

The revolved solid is a rectangular prism with a base length of

4

A hyperbola centered at the origin has vertices at

( \pm \sqrt{4}, 0)

( \pm \sqrt{9}, 0)

\newline

Write the equation of this hyperbola.

A hyperbola centered at the origin has vertices at

( \pm \sqrt{61}, 0)

( \pm \sqrt{98}, 0)

\newline

Write the equation of this hyperbola.

A hyperbola centered at the origin has vertices at

(0, \pm \sqrt{6})

(0, \pm \sqrt{74})

\newline

Write the equation of this hyperbola.

A hyperbola centered at the origin has vertices at

(0, \pm \sqrt{54})

(0, \pm \sqrt{89})

\newline

Write the equation of this hyperbola.

A hyperbola centered at the origin has vertices at

(0, \pm \sqrt{19})

(0, \pm \sqrt{55})

\newline

Write the equation of this hyperbola.

A hyperbola centered at the origin has vertices at

(0, \pm \sqrt{21})

(0, \pm \sqrt{34})

\newline

Write the equation of this hyperbola.

A hyperbola centered at the origin has vertices at

( \pm \sqrt{45}, 0)

( \pm \sqrt{70}, 0)

\newline

Write the equation of this hyperbola.

A hyperbola centered at the origin has vertices at

(0, \pm \sqrt{12})

(0, \pm \sqrt{45})

\newline

Write the equation of this hyperbola.