Question

the general form of the equation of a circle is 7x^2+7y^2-28x+42y-35=0, the equation of this circle in standard form is, the center of the cirlce is at point, and its radius is what units

Answer 1

the given equation of a circle is
$7x { }^{2} + 7y {}^{2} - 28x + 42y - 35 = 0$

simplify the equation
we get,
$x {}^{2} + y {}^{2} - 4x + 6y - 5 = 0$

the point of the centre of the circle is
2g=-(-4) 2f=-6
g=2 f=-3

therefore the points of the centre of the circle is (2,-3)

now for the radius of the circle
r=
$\sqrt{g {}^{2} - f { }^{2} + c }$

$\sqrt{4 + 9 - 5}$
$\sqrt{8}$
$2 \sqrt{2}$
radius of the circle is
$2 \sqrt{2}$