What is the standard form of an ellipsefor the equation 64x^2 - 128x + 49y^2 + 98y = 3023?

Question

Please help this is a homework problem and I dont know how to solve it????

Answer 1

You need to know how to do a Completing Square

64X^2 = (8x)^2 divide 128 / 8 / 2 = 8
add 8^2 to this expression

(8X)^2 - 128x +8^2 = 64(X-1)^2

so the full eq.
64x^2 -128x +64 + 49y^2 +98y + 49 = 3023 + 64 + 49
64(x-1)^2 +49(y+1)^2 = 3136

(x-1)^2 + (y+1)^2 = 1
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49 64