Find the equation of the ellipse with Foci (±4,0) and the major axis of length 10.

Answer 1

Based on the location of the foci, I can tell that the center of the ellipse is (0,0) and that the major axis in in the x direction. Since the major axis length is 10, a=5. I can set up this so far with this information:

x²/5²+y²/b²=1

I know from the location of the foci, that c=4. Using the following equation, I can solve for b

a²-b²=c²

5²-b²=4²

25-b²=16 Subtract 25 from both sides

-b²=-9 Divide both sides by -1

b²=9 Take the square root of both sides

3=b Plug this in

x²/5²+y²/3²=1 Simplify

x²/25+y²/9=1

Answer 2

I hope this helped!