SOLUTION: classify the conic section defined by the equation. write the standard equation of the conic section: 9x^2-90x+4y^2+16y+205=0

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: classify the conic section defined by the equation. write the standard equation of the conic section: 9x^2-90x+4y^2+16y+205=0      Log On


   

Question 83338: classify the conic section defined by the equation. write the standard equation of the conic section:
9x^2-90x+4y^2+16y+205=0
Found 2 solutions by stanbon, ayshia:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
9x^2-90x+4y^2+16y+205=0
9(x^2-10x+(10/2)^2) + 4(y^2+4y+(4/2)^2) = -205+9*25+4*4
9(x-5)^2 + 4(y+2)^2 = -205 + 225 +16 = 36
Divide thru by 36 to get:
[(x-5)^2]/4 + [(y+2)^2]/9 = 1
The conic is an ellipse.
================
Cheers,
Stan H.

Answer by ayshia(2) About Me  (Show Source):
You can put this solution on YOUR website!
9x^2-90x+4y^2+16y+205=0
9(x^2-10x+(10/2)^2) + 4(y^2+4y+(4/2)^2) = -205+9*25+4*4
9(x-5)^2 + 4(y+2)^2 = -205 + 225 +16 = 36
Divide thru by 36 to get:
(x-5)^2/4 + (y+2)^2/9 = 1
Welcome
Ayshia