6-3 Ellipses

x^2/25 + y^2/144=1
1) y is the major
2) x in the minor
3) square root of 144= +/- 12 (12,0) (-12,0)
4) square root of 25= +/- 5 (0,5) (0,-5)
5) 2 square root of 144= 24
6) 2 square root of 25= 10
7) 25-144=f^2
   -119=f^2  f= (0,square root of 119) (0,-square root of 119)

First to solve this equation, you have to have the equation in standard form.  Standard form is x^2/a^2 + y^2/b^2 =1.  The major axis is the variable with the largest denominator.  The minor axis is the variable with the smallest axis. In this equation the minor axis is x, and the major axis is y.  The vertex is the square root of the largest denominator to put in point form if the major axis is x, the answer goes in the x spot and vise versa.  The vertex of the largest denominator in this problem is +/- 12.  The other intercept is the square root of the smallest denominator and put it in point form.  The other vertex in the equation is +/- 5.  The length of the major axis is 2 times the square root of the largest denominator, and the minor axis is 2 times the square root of the smallest denominator.  In this problem, the lengths of the major and minor axis are 24 and 10.  The focus is always on the major axis and is a point.  To find the focus you have to use the formula:  smallest denominator=largest denominator-focus^2. When we solve this, we get the square root of 119.