Can you help me with this conic section problem?

Question

How do I write the equation  of the conic section with eccentricity 0.8 and Toco (1,-3) and (9,-3)

Answer 1

I assume that "Toco" meant "Foci."  The Major Axis runs horizontally, through the two foci which have common y value -3.

 

If e < 1 then c/a = 4/5 and the conic must be an Ellipse.  It helps to draw the sketch and place the foci on it; this gives 2c = 8 , c = 4 and Center (5,-3).  

 

Since c/a = 4/5 and c=4, a = 5.  Since a² - c² = b² we find that b squared is 25-16 = 9.

 

(x-5)²/25 + (y+3)²/9 = 1.