Question

What are the center and radius of the circle given by x^2 + y^2 - 16x + 8y + 4 = 0?

Answer 1

The center of the circle = (8, -4)

The radius of the circle =  $\sqrt{76}$

Finding the center and radius of a circle from the equation

The given equation of the circle is:

$x^2+y^2-16x+8y+4=0$

The equation can be expressed and simplified as:

$x^2-16x+y^2+8y=-4\\\\x^2-16y+8^2+y^2+8y+4^2=-4+8^2+4^2\\\\(x-8)^2+(y+4)^2=-4+64+16\\\\(x-8)^2+(y+4)^2=76$

The general equation of a circle is:

$(x-a)^2+(y-b)^2=r^2$

Comparing the two equations:

The center, (a, b) = (8, -4)

The radius, r = $\sqrt{76}$

Learn more on the equation of a circle here: brainly.com/question/1506955

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