The standard equation of a horizontal ellipse with center (0,0) is x^2a^2+ y^2b^2=1, where a>b>0.
x^2/121+y^2/81=1
Practice makes perfect
For an ellipse centered at the origin, we are told that the vertex is (- 11,0) and the co-vertex is (0, 9). We want to write its equation. Since the vertex lies on the x-axis, the ellipse is horizontal. Let's recall its standard equation.
x^2/a^2+y^2/b^2=1, a>b>0
Here, the major axis is horizontal, the vertices are (± a,0), and the co-vertices are (0,± b). Since we are given one vertex and one co-vertex, we know that a= 11 and that b= 9. Let's use this information to write the equation of the desired ellipse.
x^2/11^2+y^2/9^2=1 ⇔ x^2/121+y^2/81=1
