Identify the conic section from its equation.
1. (X-5)^2/4 + (y+3)^2/16 =1
2. (X-4)^2/36 - (y-2)^2/9 = 1
3. X^2+y^2+6x-16y+48=0
4. Y^2+6y-2x+13=0
5. (Y-2)^2/4 - (x+3)^2/9=0

Question

Identify the conic section from its equation.
1. (X-5)^2/4 + (y+3)^2/16 =1 
2. (X-4)^2/36 - (y-2)^2/9 = 1 
3. X^2+y^2+6x-16y+48=0 
4. Y^2+6y-2x+13=0 
5. (Y-2)^2/4 - (x+3)^2/9=0

mathmale · Answer

$$(x-5)^{2}/4 + (y+3)^{2}/16 = 1       => (x-5)^{2}/2^{2}+(y+3)^{2}/16 = 1$$

matches the general equation of an ellipse:

mathmale · Answer

$$(x-h)^{2}/a ^{2}+(y-k)^{2}/b ^{2} = 1$$

mathmale · Answer

So the given equation #1 is the equation of an ellipse centered at (5,-3) with major axis 4 and minor axis 2.  That is, the ellipse is a vertical one; the distance from one vertex to the other, vertically, is 2(4) = 8.