Question

Centre of ellipse 16x2 + 25y2 32x 100y 284 = 0, is:

Answer 1

$16 {x}^{2} + 25 {y}^{2} + 32x + 100y - 284 = 0 \\ 16( {x}^{2} + 2x + 1) + 25( {y}^{2} + 4y + 4) = 284 + 116 \\ 16 {(x + 1)}^{2} + 25 {(y + 2)}^{2} = 400 \\ \frac{ {(x + 1)}^{2} }{25} + \frac{ {(y + 2)}^{2} }{16} = 1 \\ this \: is \: the \: standard \: form \: of \: ellipse \: \\ with \: centre \: ( - 1 \: . \: - 2)$
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