Question

is the ellipse represented by the equation (x-5)^2/3 + (y+1)^2/5 =1 oriented horizontally or vertically? explain how you know

Answer 1

Hello from MrBillDoesMath!

Answer:  Vertical

Discussion:

Generally, consider the ellipse

x^2/ a^2 + y^2/b^2 = 1

If a^2 > b^2, the ellipse is horizontal; otherwise vertical.

In our case, a^2 =3 and b^2 = 5 so  a^2 < b^2. The ellipse is vertical

Thank you,

MrB

Answer 2

Answer:

The orientation will be vertical.

Step-by-step explanation:

An ellipse can have both a horizontal and vertical orientation. There are always two foci that are on the major axis. The major axis is the longest of the two axes that pass through the center of an ellipse. The vertices are also located on the major axis, which are the endpoints of the ellipse and the points that are farthest from each other in an ellipse. The shortest axis that passes through the center is called the minor axis, our endpoints are called co-vertices.

On the other hand, 2a is the length of the major axis, so the value "a" is called the semi-major axis. 2b is the length of the minor axis, so "b" is the length of the minor axis.

Given that it is always greater than b, and that h and k are the center of the vertex, the equation of the ellipse is:

$\frac{(x-h)^{2} }{a^{2} } +\frac{(y-k)^{2} }{b^{2} }=1$

This is for parallel ellipses ale axis "x". That is, the major axis is the "x" axis with a length of 2a. The minor axis is the "y" axis with a length of 2b.   And the orientation will be horizontal.

$\frac{(x-h)^{2} }{b^{2} } +\frac{(y-k)^{2} }{a^{2} }=1$

This is for parallel ellipses ale axis "y". That is, the major axis is the "y" axis with a length of 2a. The minor axis is the x axis with a length of 2b.  And the orientation will be vertical.

In this case you have:

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

3 is less than 5, so a² has to be the value of 5 and b² must be worth 3. This is so since, as mentioned a is always greater than b, then by raising it to the power it is also true that a² is greater that b².

Following the equation model outlined above (where the center in this case is located at "x "= 5 and "y" = - 1), the major axis is the "y" axis with a length of 2a. The minor axis is the x axis with a length of 2b.  So the orientation will be vertical.