The equation of a vertical ellipse is x^2b^2+ y^2a^2=1. The equation of a horizontal ellipse is x^2a^2+ y^2b^2=1. In both cases a and b are positive numbers, with a>b.
x^2/169+y^2/144=1
Practice makes perfect
Since the given focus is on the x-axis, the ellipse is horizontal. Recall the general equation for this type of ellipse.
x^2/a^2+y^2/b^2=1, a>b>0
Here, the vertices are (± a,0) and the co-vertices (0,± b). If we let (± c,0) be the foci of our horizontal ellipse, we can write an equation connecting a, b, and c.
c^2=a^2-b^2
We are told that the point (- 5,0) is a focus and the point (0,- 12) is a co-vertex. Therefore c=5 and b= 12. Let's substitute these values into the above equation to find the value of a.
Note that we only took the principal root because a is the absolute value of the nonzero coordinate of the vertices. Now that we know that a= 13, we can finally write the equation of the ellipse.
x^2/13^2+y^2/12^2=1 ⇔ x^2/169+y^2/144=1
