Question

2) [7.2] Complete the square and graph the Ellipse: Give the center, foci and vertices. (7 points) 4x² + y2-16x-6y =15| Center: Foci: Vertices:

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Answer 1

a2 6? b 4x?ty=-163-6ý = 15 Standard equation (2-h) ? +4-K) ² = 1 Center Thik) and a,b are semi-major & semi minor ani's Rewrite 46x²4x) +(4²6y)=15 . {Factor out? . (x²-4x) + + (y²-by) = 151 § divide by 4} (2244+45++(y=67) = 15 74 { convert x to (2-2)² + + Ly by + 9) = 15 +4 +92 { convert y to square form } (24-2]2+ (4-3)2 = 10 square form} (2-2) + (-3) = 1 (3-2) + (9-3)2 =1 (TO) ² 120100² Center (hik) = {(2,3), (and a To Foci (h, K+c), Ch, K-c) C=V62-Q? - v30 Foci - (2,3+130), (2, 3-130) vertice Ch,kto), Ch,kab)- = |( 23+2V10) , (2, 3-250) b2vio Scanned with CamScanner

Plott = 1 -10