Question

tutorial exercise
find an equation of the circle that satisfies the given conditions. write your answer in standard form.
center $(4,-7)$, radius 7
step 1
recall that the standard form of the equation of a circle with center at $(h, k)$ and radius $r$ is
$$(x-(square))^{2}+(y-(square))^{2}=(square)^{2}.$$

Explanation:

Step1: Recall the standard form of the circle equation

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

Step2: Substitute the given values

Here, \(h = 4\), \(k=-7\), and \(r = 7\). Substituting these into the formula, we get \((x - 4)^2+(y-(-7))^2=7^2\).

Step3: Simplify the equation

Simplify \(y-(-7)\) to \(y + 7\). So the equation is \((x - 4)^2+(y + 7)^2 = 49\).

Answer:

\((x - 4)^2+(y + 7)^2 = 49\)