Question

15 POINT, need this answered ASAP

Answer 1

Option A

The equation of ellipse in standard form is $\frac{x^{2}}{9}+\frac{y^{2}}{4}=1$

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 $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$

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:

$\begin{array}{l}{\rightarrow \frac{x^{2}}{(-3)^{2}}+\frac{y^{2}}{2^{2}}=1} \\\\ {\rightarrow \frac{x^{2}}{9}+\frac{y^{2}}{4}=1}\end{array}$

Hence, the standard form equation is $\frac{x^{2}}{9}+\frac{y^{2}}{4}=1$

Thus option A is correct