Question

What is an equation in standard form of an ellipse centered at the origin with vertex (-6,0) and co-vertex (0,4)?

Answer 1

i can show the answers if needed but i want to know how to do it

Answer 2

What is the standard form of an ellipse centered on the origin?

Answer 3

i dont know

Answer 4

Isn't it something like
\[\frac{ x^2 }{ a^2 }+\frac{ y^2 }{ b^2 }=1\]

Answer 5

idk tbh ive been slacking off all year

Answer 6

It is. I am just trying to get you to think about it. You should probably review the topic and then approach the problem again.

Answer 7

i dont have time to review the topic, the semester ends tonight

Answer 8

what do you do to the equation?

Answer 9

Let's draw a picture.

Answer 10

okay so how do you write an equation based on the vertexes?

Answer 11

The major axis is the a value in the equation and that is equal to 6 since the vertex is 6 units from the origin. The y value is 4 which is the b value in the equation and it is the minor axis. So now you have enough information to complete the equation.

Answer 12

i dont know what major and minor axis means?

Answer 13

so they just mean x and y axis

Answer 14

when putting them into equation are they x and y?

Answer 15

Yes so
a=6
b=4
\[\frac{ ^{x^2} }{ a^2 }+\frac{ y^2 }{ b^2 }=1\]

Answer 16

so x^2/6^2+y^2/4^2=1? is that it or do you have to do more or simplify the denominator

Answer 17

I would simply, but you got it right
\[\frac{ x^2 }{ 36 } + \frac{ y^2 }{ 16 }=1\]

Answer 18

oh ok thank you. thank you for your patience as well

Answer 19

You are welcome :)