Question

now, try this problem. derive the equation of a circle with a center at (6, -8) and a radius of 8 units. move one answer to each box to complete the sentences. the horizontal distance between a point (x, y) on the circle and the center is (x - 6)^2+(y + 8)^2×. the vertical distance between the same point on the circle and the center is |y + 8|√. substituting these distances into the pythagorean theorem and squaring the radius gives

Explanation:

Step1: Recall circle - equation formula

The standard form of the equation of a circle with center \((h,k)\) and radius \(r\) is \((x - h)^2+(y - k)^2=r^2\). Here, \(h = 6\), \(k=-8\), and \(r = 8\).

Step2: Substitute values into formula

Substitute \(h = 6\), \(k=-8\), and \(r = 8\) into the formula. We get \((x - 6)^2+(y-(-8))^2=8^2\), which simplifies to \((x - 6)^2+(y + 8)^2=64\).

Answer:

\((x - 6)^2+(y + 8)^2=64\)