Find the quation for the conic described
Ellipse with foci at (0,+3) and endpoints of the major axis at (0,+4)
p.s. the +3 and +4 are also  I just did not know how to type a + and  together.
Thank You!
Ellipse with foci at (0,+3) and endpoints of the major axis at (0,+4)
p.s. the +3 and +4 are also  I just did not know how to type a + and  together.
Thank You!

The center is at the originit is halfway between the foci along the focal axis (here the yaxis). If the equation is
x²/a² + y²/b² = 1
and the foci are at (0, ±3), then b = 4 and
a = √(b²  3²) = √(16  9) = √(7).
The equation is therefore
x²/7 + y²/16 = 1.
x²/a² + y²/b² = 1
and the foci are at (0, ±3), then b = 4 and
a = √(b²  3²) = √(16  9) = √(7).
The equation is therefore
x²/7 + y²/16 = 1.