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 center at the origin, vertex $(-9,0)$ , and co-vertex $(0,3)$ .

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 center at the origin, vertex

(-9,0)

, and co-vertex

(0,3)

.

Identify Vertex Value: Identify the value of $a$ using the vertex. $\newline$ Vertex: $(-9, 0)$ $\newline$ $a =$ distance from center to vertex $\newline$ $a = \sqrt{((-9 - 0)^2 + (0 - 0)^2)}$ $\newline$ $a = \sqrt{81}$ $\newline$ $a = 9$
Identify Co-vertex Value: Identify the value of $b$ using the co-vertex. $\newline$ Co-vertex: $(0, 3)$ $\newline$ $b =$ distance from center to co-vertex $\newline$ $b = \sqrt{(0 - 0)^2 + (3 - 0)^2}$ $\newline$ $b = \sqrt{9}$ $\newline$ $b = 3$
Write Standard Form Equation: Write the standard form equation of the ellipse. $\newline$ Center: $(0, 0)$ $\newline$ $a = 9$ , $b = 3$ $\newline$ Standard form: $\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1$ $\newline$ Plug in $h = 0$ , $k = 0$ , $a = 9$ , and $b = 3$ : $\newline$ $\frac{(x - 0)^2}{9^2} + \frac{(y - 0)^2}{3^2} = 1$ $\newline$ $x^2/81 + y^2/9 = 1$

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 2 months ago

Question

Write the equation in standard form for the ellipse

7x^2 + y^2 = 21

\newline

Posted 3 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 2 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 2 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 3 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 4 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 4 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 4 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 4 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 4 months ago