SOLUTION: 11x^2+17y^2+484x+442y+7636=0 Identify if the equation is a hyperbola, parabola, or ellipse and label the center point, vertex points, focus points, asymptote equations, a length,

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: 11x^2+17y^2+484x+442y+7636=0 Identify if the equation is a hyperbola, parabola, or ellipse and label the center point, vertex points, focus points, asymptote equations, a length,       Log On


   

Question 927906: 11x^2+17y^2+484x+442y+7636=0
Identify if the equation is a hyperbola, parabola, or ellipse and label the center point, vertex points, focus points, asymptote equations, a length, b length, and c length, and the transverse axis.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
11x%5E2%2B17y%5E2%2B484x%2B442y%2B7636=0
%2811x%5E2%2B484x%29%2B%2817y%5E2%2B442y%29%2B7636=0
11%28x%5E2%2B44x%29%2B17%28y%5E2%2B26y%29%2B7636=0.............complete square
11%28x%5E2%2B44x%2B__%29%2B17%28y%5E2%2B26y%2B___%29%2B7636=0+

11%28x%2B22%29%5E2-5324%2B17%28y%2B13%29%5E2%29-2873%2B7636=0+
11%28x%2B22%29%5E2%2B17%28y%2B13%29%5E2%29-8197%2B7636=0+
11%28x%2B22%29%5E2%2B17%28y%2B13%29%5E2%29-561=0+
11%28x%2B22%29%5E2%2B17%28y%2B13%29%5E2%29=561
%2811561%29%2F%28x%2B22%29%5E2%2B%2817%2F561%29%28y%2B13%29%5E2%29=561%2F561
%28x%2B22%29%5E2%2F51%2B%28y%2B13%29%5E2%29%2F33=1
ellipse
center is at (-22,-13)
a=sqrt%2851%29..=>..a=7.14143 semimajor axis length
b=sqrt%2833%29..=>..b=5.74456 semiminor axis length

foci | ((-22-3sqrt%282%29,+-13) | (-22%2B3+sqrt%282%29, -13)),approx.((-26.2426, -13) | (-17.7574, -13))
vertices | ((-22-sqrt%2851%29, -13) | (-22%2Bsqrt%2851%29, -13)),approx.((-29.1414, -13) | (-14.8586, -13))
focal parameter | 11%2Fsqrt%282%29, approx. 7.77817
eccentricity | sqrt%286%2F17%29,approx. 0.594089