Question

Write the equation of the ellipse shown in the graph.
A.(x+1)^2/4 + (y-2)^2/9=1
B.(x+1)^2/9 + (y-2)^2/4=1
C.(x-1)^2/4 + (y+2)^2/9=1
D.(x-1)^2/9 + (y+2)^2/4=1

Answer 1

Answer:

A. $\frac{(x+1)^{2}}{4}+\frac{(y-2)^{2}}{9} =1$  

Step-by-step explanation:        

We have been given a graph and we are asked to write an equation for the ellipse shown in the graph.

Since we know that standard equation for ellipse is in form: $\frac{(x-h)^{2}}{a^{2}}+\frac{(y-k)^{2}}{b^{2}} =1$, where our ellipse is centered at (h,k), whose horizontal radius is a and vertical radius is b.

We can see from our diagram that center of our given ellipse is at point(-1,2)

We can see that our ellipse has a vertical radius of 5-2=3 units. The horizontal radius of our ellipse is $1-(-1)=1+1=2$ units long.  

Now let us substitute our given values in standard ellipse equation to find the correct option.

$\frac{(x-h)^{2}}{a^{2}}+\frac{(y-k)^{2}}{b^{2}} =1$,

$\frac{(x--1)^{2}}{2^{2}}+\frac{(y-2)^{2}}{3^{2}} =1$    

$\frac{(x+1)^{2}}{4}+\frac{(y-2)^{2}}{9} =1$

Upon looking at our given options we can see that option A is the correct choice.