What conic section is #25x^2 + 100x + 9y^2 – 18y = 116#?

1 Answer
Mar 8, 2016

Answer:

Ellipse

Explanation:

If a, b and 2h are the coefficients of the terms in #x^2. y^2#and xy, then the second degree equation represents en ellipse parabola or hyperbola according as #ab-h^2# >. = or < 0.
Here, #ab-h^2# = 225 > 0.

The equation can be reorganized as
#(x+2)^2/9 +(y-1)^2/25#= 1.

Center C of the ellipse is #(-2,1)#.
Semi axes a = 5 and b = 3.
Major axis is #x=-2# is parallel to y-axis.
Eccentricity e = #sqrt(9^2-5^2)/5=2sqrt14/5#.
For foci S and S', CS = CS' = ae = #sqrt14#.
Foci: #(-2, 1+sqrt14) and (-2,1 -sqrt14)#