Question

What is the diameter of a circle with the equation (x 6)2 (y − 4)2 = 16?.

Answer 1

The diameter of the circle with the provided equation of circle which has radius 4 units is 2 units long.

What is the equation of circle?

The equation of the circle is the equation which is used to represent the circle in the algebraic equation form with the value of center point in the coordinate plane and measure of radius.

The standard form of the equation of the circle can be given as,

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

Here (h,k) is the center of the circle and (r) is the radius of the circle.

The equation given  in the problem is

$(x+ 6)^2 +(y - 4)^2 = 16$

Make it like equation of circle as,

$(x+ 6)^2 +(y - 4)^2 = (4)^2$

Let's compare it with the equation of circle we get,

$h=-6\\k=4\\r=4$

Here, the radius of the circle is 4 units. As the radius of the circle is twice the diameter of the circle. Thus, the Diameter of the circle is,

$d=\dfrac{4}{2}\\d=2$

Hence, the diameter of the circle with the provided equation of circle which has radius 4 units is 2 units long.

Learn more about the equation of circle here;

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