15 POINT, need this answered ASAP Write an equation of an ellipse in standard form with the center at the origin and with the given characteristics. vertex at (-3,0) and co-vertex (0,2) a. x^2/9+y^2/4=1 b. x^2/4+y^2/9=1c. x^2/3+y^2/9=1d. x^2/2+y^2/3=1

Option AThe equation of ellipse in standard form is [tex]\frac{x^{2}}{9}+\frac{y^{2}}{4}=1[/tex]Solution:Given, We have to write an equation of an ellipse in standard form with the center at the originGiven that vertex at (-3,0) and co-vertex (0,2) The standard form of an ellipse is [tex]\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1[/tex]where a is x- intercept and b is y – intercept. We have vertex (-3, 0) and (0, 2) from these we can say that, x – intercept is – 3 and y – intercept is 2 . As we know that intercepts are the respective values when other variables becomes 0. Now, let us find our ellipse equation:[tex]\begin{array}{l}{\rightarrow \frac{x^{2}}{(-3)^{2}}+\frac{y^{2}}{2^{2}}=1} \\\\ {\rightarrow \frac{x^{2}}{9}+\frac{y^{2}}{4}=1}\end{array}[/tex]Hence, the standard form equation is [tex]\frac{x^{2}}{9}+\frac{y^{2}}{4}=1[/tex]Thus option A is correct