How do you convert 4x²+y²-8x+4y-9=0 into standard form?

May 11, 2016

Perform a double completion of squares.

Explanation:

$4 \left({x}^{2} - 2 x + 1 - 1\right) + \left({y}^{2} + 4 + 4 - 4\right) - 9 = 0$

$4 {\left(x - 1\right)}^{2} - 4 + {\left(y + 2\right)}^{2} - 4 - 9 = 0$

$4 {\left(x - 1\right)}^{2} + {\left(y + 2\right)}^{2} = 17$

Hopefully this helps!