Question

A. 1

Answer 1

Step-by-step explanation:

Given equation of circle (in general form) is:

$8 {x}^{2} + 8 {y}^{2} - 16x - 32y + 24 = 0 \\ \\ dividing \: throughout \: by \: 8 \: we \: find : \\ {x}^{2} + {y}^{2} - 2x - 4y + 3 = 0 \\ equating \: it \: with : \\ {x}^{2} + {y}^{2} + 2gx + 2fy + c = 0 \\ 2g = - 2 \implies \: g = - 1\\ 2f = - 4 \implies \: f = - 2 \\ c = 3 \\ \therefore \:center = ( - g, \: \: - f) = (1, \: \: 2) \\ \\ radius \: r = \sqrt{ {g}^{2} + {f}^{2} - c } \\ = \sqrt{ {1}^{2} + {2}^{2} - 3} \\ = \sqrt{1 + 4 - 3} \\ = \sqrt{5 - 3} \\ = \sqrt{2} \: units$