# SOLUTION: What are the vertices and the foci of this conic. 9x^2+ 4y^2 + 64y = -220 I basically need the most help with how to solve it, not just simply the answer please. Thank you

Algebra ->  Algebra  -> Quadratic-relations-and-conic-sections -> SOLUTION: What are the vertices and the foci of this conic. 9x^2+ 4y^2 + 64y = -220 I basically need the most help with how to solve it, not just simply the answer please. Thank you       Log On

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 Click here to see ALL problems on Quadratic-relations-and-conic-sections Question 542265: What are the vertices and the foci of this conic. 9x^2+ 4y^2 + 64y = -220 I basically need the most help with how to solve it, not just simply the answer please. Thank you Answer by lwsshak3(6742)   (Show Source): You can put this solution on YOUR website!What are the vertices and the foci of this conic. 9x^2+ 4y^2 + 64y = -220 I basically need the most help with how to solve it, not just simply the answer please. ** 9x^2+ 4y^2 + 64y = -220 complete the square 9x^2+4(y^2+16y+64)=-220+256=36 9x^2+4(y+8)^2=36 divide by 36 x^2/4+(y+8)^2/9=1 This is an equation of an ellipse with vertical major axis of the standard form: (x-h)^2/b^2+(y-k)^2/a^2=1,a>b, with (h,k) being the (x,y) coordinates of the center. .. For given problem: Center:(0,-8) a^2=9 a=√9=3 vertices: (0,-8±a)=(0,-8±3)=(0,-11) and (0,-5) .. b^2=4 .. c^2=a^2-b^2=9-4=5 c=√5≈2.24 Foci: (0,-8±c)=(0,-8±√5)=(0,-10.24) and (0,-5.76)