Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Write the equation in standard form for the ellipse with vertices $(-11,0)$ and $(11,0)$ , and co-vertices $(0,2)$ and $(0,-2)$ .

View step-by-step help

View step-by-step help

Write equations of ellipses in standard form using properties

Full solution

Q. Write the equation in standard form for the ellipse with vertices

(-11,0)

and

(11,0)

, and co-vertices

(0,2)

and

(0,-2)

.

Calculate semi-major axis: Vertices are $(-11, 0)$ and $(11, 0)$ , so the major axis is horizontal and the length of the major axis is $2a$ , where $a$ is the semi-major axis. $\newline$ Calculate $a$ : $a = 11$ (since the vertex is $11$ units away from the center at the origin).
Calculate semi-minor axis: Co-vertices are $(0, 2)$ and $(0, -2)$ , so the minor axis is vertical and the length of the minor axis is $2b$ , where $b$ is the semi-minor axis. $\newline$ Calculate $b$ : $b = 2$ (since the co-vertex is $2$ units away from the center at the origin).
Standard form equation: The standard form of the equation for an ellipse with a horizontal major axis is $(x-h)^2/a^2 + (y-k)^2/b^2 = 1$ , where $(h, k)$ is the center of the ellipse. $\newline$ Since the center is at the origin, $h = 0$ and $k = 0$ .
Plug in values and simplify: Plug in the values of $a$ and $b$ into the standard form equation. $\newline$ Equation: $\frac{(x-0)^2}{11^2} + \frac{(y-0)^2}{2^2} = 1$ $\newline$ Simplify the equation: $\frac{x^2}{121} + \frac{y^2}{4} = 1$

More problems from Write equations of ellipses in standard form using properties

Question

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

(-10,0)

, and co-vertex

(0,3)

Posted 7 months ago

Question

Write the equation in standard form for the ellipse

7x^2 + y^2 = 21

\newline

Posted 9 months ago

Question

What is the center of the ellipse

x^2 + 2y^2 - 16 = 0

\newline

Write your answer in simplified, rationalized form.

\newline

(\_\_\_\_\_,\_\_\_\_\_)

Posted 7 months ago

Question

What is the length of the major axis of the ellipse

\frac{x^2}{9} + \frac{y^2}{2} = 1

\newline

Write your answer in simplified, rationalized form.

\newline

\_\_\_\_\_

Posted 7 months ago

Question

What is the center of the ellipse

\left(\frac{(x - 5)^2}{9}\right) + \left(\frac{(y - 2)^2}{54}\right) = 1

\newline

Write your answer in simplified, rationalized form.

\newline

(________ , _______)

Posted 9 months ago

Question

The equation of an ellipse is given below.

\newline

\frac{(x+15)^{2}}{676}+\frac{(y-4)^{2}}{100}=1

\newline

What are the foci of this ellipse?

\newline

1

\newline

(-15+\sqrt{24}, 4)

(-15-\sqrt{24}, 4)

\newline

(-15,4+\sqrt{24})

(-15,4-\sqrt{24})

\newline

(-39,4)

(9,4)

\newline

(-15,28)

(-15,-20)

Posted 9 months ago

Question

The equation of an ellipse is given below.

\newline

\frac{(x-5)^{2}}{3}+\frac{(y-7)^{2}}{6}=1

\newline

What are the foci of this ellipse?

\newline

1

\newline

(5,7+\sqrt{3})

(5,7-\sqrt{3})

\newline

(-5,-7+\sqrt{3})

(-5,-7-\sqrt{3})

\newline

(-5+\sqrt{3},-7)

(-5-\sqrt{3},-7)

\newline

(5+\sqrt{3}, 7)

(5-\sqrt{3}, 7)

Posted 9 months ago

Question

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)

Posted 9 months ago

Question

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

( \pm 12,0)

and vertices at

( \pm 13,0)

Posted 9 months ago

Question

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

(0, \pm 6)

and vertices at

(0, \pm \sqrt{37})

Posted 9 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant