Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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. $\newline$ $\_\_$

View step-by-step help

View step-by-step help

Find properties of ellipses from equations in general form

Full solution

Q. 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

\_\_

Identify Values: First, let's identify the values of $a^2$ and $b^2$ from the equation of the ellipse. The equation is in the form $(x^2)/a^2 + (y^2)/b^2 = 1$ , where $a^2$ is the larger denominator.
Find $a$ and $b$ : In our equation, $\frac{x^2}{9} + \frac{y^2}{2} = 1$ , we see that $a^2 = 9$ and $b^2 = 2$ . Since $9 > 2$ , $a^2$ corresponds to the major axis.
Calculate $a$ : Now, we find the value of $a$ by taking the square root of $a^2$ . So, $a = \sqrt{9} = 3$ .
Major Axis Length: The length of the major axis is $2$ times the value of $a$ , which means it's $2 \times 3 = 6$ .

More problems from Find properties of ellipses from equations in general form

Question

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

(-10,0)

, and co-vertex

(0,3)

Posted 1 month ago

Question

Write the equation in standard form for the ellipse

7x^2 + y^2 = 21

\newline

Posted 2 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 1 month 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 1 month 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 2 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 3 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 3 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 3 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 3 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 3 months ago