i was wondering how to solve this math question?

Question

x^2+(y^2/4)=1
is this an ellipse or hyperbola?what point is it centered at? wat are all of the vertices. and wat are all of the asymptotes? i would greatly appreciate anyone who could tell me how to do it not just the answer. thank you all

Answer 1

This is an ellipse with a =2 and b=1 and c= sqrt(3).
The foci are located at (0,sqrt(3) and (0, -sqrt(3)
The vertices are at (0,2) and (0,-2)
The ends of the minor axis are at (-1,0) and (1,0).
It is centered at the origin.
The equation takes the form x/b^2 +y/a^2 = 1 since the major axis on the y-axis.
If the major axis were on the x-axis, the equation would be
x^2/a^ +y^2/b^2= 1
b^2 = a^2-c^2 so a must be greater than b
2a is the sum of the distances from any point on the ellipse to the foci. The distance between the foci is 2c.
There are no asymptotes.

If the ellipse has a center at (h,k) and the major axis is parallel to x-axis, the equation is (x-h)^2/a^2 +(y-k)^2/b^2=1
If the ellipse has a center at (h,k) and the major axis is parallel to y-axis,the equation is (x-h)^2/b^2 +(y-k)^2/a^2=1

Answer 2

Okay, the formula of the Ellipse:

a. the major axis is horizontal: (x-h)^2/a^2 + (y-k)^2/b^2=1

b. the major axis is vertical: (x-h)^2/b^2 + (y-k)^2/a^2=1

the formula for Hyperbola:

a. Transverse axis is horizontal: (x-h)^2/a^2 - (y-k)^2/b^2=1
b. Transverse axis is vertical: (y-k)^2/a^2 - (x-h)^2/b^2=1

by compairing x^2+y^2/4=1 to the formulas above, you can conclude that the figure of your problem is Ellipse. The center is (0,0) because there are no h or k stay next to x or y.

The next one is finding the major axis and minor.

a. major: radical of 4= 2. Start from the origin. count up 2 units, and count down 2.
b. Minor: radical of 1= 1( the denominator of x^2). Start from the origin. count to right 1 unit and to the left 1.
be sure to mark all the points. after that draw the ellipse by the points.

Hard to explain by internet unless i can talk directly to you. But i hope this would work for you!!!!!!! good luck!!!!!!!!

Answer 3

http://www.mathwarehouse.com/ellipse/focus-of-ellipse.php