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Write equations of ellipses in standard form using properties

Write the equation in standard form. Then identify the center and radius.

\newline

13

x^{2}+y^{2}+8 x-6 y-25=0

Write the equation in standard form for the ellipse with center at the origin, vertex

(-10,0)

, and co-vertex

(0,3)

A B C D

is a trapezoid with midsegment

E F

, find its perimeter.

Write the equation in standard form for the ellipse with vertices

(-7,0)

(7,0)

, and co-vertices

(0,4)

(0,-4)

Write the equation in standard form for the ellipse with vertices

(0,10)

(0,-10)

, and co-vertices

(-2,0)

(2,0)

Write the equation in standard form for the ellipse with center at the origin, vertex

(0,9)

, and co-vertex

(-8,0)

Write the equation in standard form for the ellipse with center at the origin, vertex

(-9,0)

, and co-vertex

(0,3)

Write the equation in standard form for the ellipse with vertices

(-3,0)

(3,0)

, and co-vertices

(0,2)

(0,-2)

Write the equation in standard form for the ellipse with vertices

(-9,0)

(9,0)

, and co-vertices

(0,5)

(0,-5)

Write the equation in standard form for the ellipse with center at the origin, vertex

(0,6)

, and co-vertex

(-5,0)

Write the equation in standard form for the ellipse with vertices

(-11,0)

(11,0)

, and co-vertices

(0,2)

(0,-2)

Write the equation in standard form for the ellipse with center at the origin, vertex

(-11,0)

, and co-vertex

(0,5)

Write the equation in standard form for the ellipse with vertices

(0,12)

(0,-12)

, and co-vertices

(-4,0)

(4,0)

Find the center and foci of the ellipse:

\newline

4x^{2}+9y^{2}+8x-36y+4=0

Write an equation for an ellipse centered at the origin, which has foci at

(0, \pm 6)

and vertices at

(0, \pm 10)

Write an equation for an ellipse centered at the origin, which has foci at

(0, \pm 2)

and vertices at

(0, \pm \sqrt{15})

Write an equation for an ellipse centered at the origin, which has foci at

( \pm 5,0)

and vertices at

( \pm \sqrt{41}, 0)

Write an equation for an ellipse centered at the origin, which has foci at

( \pm \sqrt{3}, 0)

and co-vertices at

(0, \pm 9)

Write an equation for an ellipse centered at the origin, which has foci at

(0, \pm 3)

and co-vertices at

( \pm 2,0)

Write an equation for an ellipse centered at the origin, which has foci at

( \pm 8,0)

and vertices at

( \pm 17,0)

Write an equation for an ellipse centered at the origin, which has foci at

(0, \pm 15)

and vertices at

(0, \pm 25)

Write an equation for an ellipse centered at the origin, which has foci at

(0, \pm \sqrt{63})

and vertices at

(0, \pm \sqrt{91})

Write an equation for an ellipse centered at the origin, which has foci at

(0, \pm \sqrt{15})

and co-vertices at

( \pm \sqrt{21}, 0)

Write an equation for an ellipse centered at the origin, which has foci at

( \pm \sqrt{12}, 0)

and vertices at

( \pm \sqrt{37}, 0)

The equation of an ellipse is given below.

\newline

\frac{x^{2}}{67}+\frac{y^{2}}{57}=1

\newline

What are the foci of this ellipse?

\newline

1

\newline

(10,0)

(-10,0)

\newline

(0,10)

(0,-10)

\newline

(\sqrt{10}, 0)

(-\sqrt{10}, 0)

\newline

(0, \sqrt{10})

(0,-\sqrt{10})

Write an equation for an ellipse centered at the origin, which has foci at

(0, \pm 24)

and co-vertices at

( \pm 10,0)

Write an equation for an ellipse centered at the origin, which has foci at

(0, \pm \sqrt{62})

and co-vertices at

( \pm 5,0)

Write an equation for an ellipse centered at the origin, which has foci at

( \pm \sqrt{8}, 0)

and co-vertices at

(0, \pm \sqrt{10})

Write an equation for an ellipse centered at the origin, which has foci at

(0, \pm \sqrt{55})

and vertices at

(0, \pm \sqrt{89})

Write an equation for an ellipse centered at the origin, which has foci at

( \pm 3,0)

and co-vertices at

(0, \pm 4)

The equation of an ellipse is given below.

\newline

\frac{x^{2}}{15}+\frac{(y-5)^{2}}{20}=1

\newline

What are the foci of this ellipse?

\newline

1

\newline

(0,10)

(0,0)

\newline

(0,5+\sqrt{5})

(0,5-\sqrt{5})

\newline

(5,5)

(-5,5)

\newline

(0+\sqrt{5}, 5)

(0-\sqrt{5}, 5)

Write an equation for an ellipse centered at the origin, which has foci at

( \pm \sqrt{13}, 0)

and co-vertices at

(0, \pm 11)

Write an equation for an ellipse centered at the origin, which has foci at

(0, \pm 15)

and co-vertices at

( \pm 8,0)

Write an equation for an ellipse centered at the origin, which has foci at

(0, \pm \sqrt{14})

and co-vertices at

( \pm \sqrt{2}, 0)

Write an equation for an ellipse centered at the origin, which has foci at

(0, \pm 6)

and vertices at

(0, \pm \sqrt{37})

Write an equation for an ellipse centered at the origin, which has foci at

( \pm 12,0)

and vertices at

( \pm 13,0)

The equation of an ellipse is given below.

\newline

\frac{x^{2}}{46}+\frac{(y+8)^{2}}{26}=1

\newline

What are the foci of this ellipse?

\newline

1

\newline

(0+\sqrt{20}, 8)

(0-\sqrt{20}, 8)

\newline

(0,8+\sqrt{20})

(0,8-\sqrt{20})

\newline

(0,-8+\sqrt{20})

(0,-8-\sqrt{20})

\newline

(0+\sqrt{20},-8)

(0-\sqrt{20},-8)

Write the equation in standard form for the ellipse with center at the origin, vertex

(-10,0)

, and co-vertex

(0,3)