Option A
The 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 origin
Given 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
