SOLUTION: what is the equation for the conic section? it is an ellipse with the vertices (-2,4) and (-2,-6). covertices are (-4,-1) and (0,-1). and what are the foci?

what is the equation for the conic section? it is an ellipse with the vertices
(-2,4) and (-2,-6). covertices are (-4,-1) and (0,-1). and what are the foci? 


Plot those 4 points:
 

 
Connect them to show the major and minor axes
of the ellipse:
 

 
Sketch in the ellipse:
 


Since the ellipse has its major axis vertical,
it has the standard form:
 

 
where 
 
1. (h,k) = the center 
 
2. a = the distance from the center to either of the two vertices
 
3. b = the distance from the center to either of the the covertices.
 
We can see from the graph that 
 
1. the center of the ellipse is (h,k) = (-2,-1)
 
2. a = 5
 
3. b = 2
 
So the equation 
 

 
becomes
 

 
or
 


to find the foci, we calculate c by
this Pythagorean relation:











The two foci are on the major axis c usits
from the center, so they are

(-2,-1+) and (-2,-1-)

 
Edwin