# How do you write an equation for an ellipse in standard form with the center at the origin and with characteristics of height of 12 units and width of 19 units?

the equation of an ellipse is ${x}^{2} / {a}^{2} + {y}^{2} / {b}^{2} = 1$ where a is the radius of the x-axis and b is the radius of the y-axis, so the height would be the y-axis radius multiplied by 2. So b=6 and b^2=36. Using that same idea the a would equal 9 and a^2= 81. Therefore, ${x}^{2} / 81 + {y}^{2} / 36 = 1$ would be the equation you're looking for.