Question

find centre and radius of circle x square +y sq. - 8x+ 10 Y - 12=.

Answer 1

${x}^{2} + {y}^{2} - 8x + 10y - 12 = 0$
${x}^{2} + {y}^{2} + 2( - 4)x + 2(5)y - 12 = 0$
This is of the form:
${x}^{2} + {y}^{2} + 2gx + 2fy + c = 0$
Thus,
Coordinates of the center are:
(-g,-f)=(4,-5)
Radius is:
$\sqrt{ {g}^{2} + {f}^{2} - c }$
$= \sqrt{ {4}^{2} + {5}^{2} + 12}$
$= \sqrt{16 + 25 + 12}$
$\sqrt{53}$

Answer 2

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