Question

A circle is described by the equation x2 y2 14x 2y 14 = 0. What are the coordinates for the center of the circle and the length of the radius? A. (-7, -1), 36 units B. (7, 1), 36 units C. (7, 1), 6 units D. (-7, -1), 6 units.

Answer 1

The center of the circle is (-7,-1) and the length of the radius of the circle is 6 units.

What is the general form of the equation of a circle?

We know that the general form of a circle is written as,

$(x-h)^2+(y-k)^2 = R^2$

where, (h,k) is the coordinates of the center of the circle and R is the radius of the circle.

What are the coordinates for the center of the circle and the length of the radius?

We know the general form of the equation of a circle, substitute the values and solve the equation to get the same equation,

$(x-h)^2+(y-k)^2 = R^2$

$[x-(-7)]^2+[y-(-1)]^2 = 6^2\\\\(x+7)^2+(y+1)^2 = 36\\\\x^2+49+14x+y^2 +1+2y =36\\\\x^2+y^2+14x+2y+14 = 0$

Hence, the center of the circle is (-7,-1) and the length of the radius of the circle is 6 units.

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