Problem 36 - College Algebra

Question

Write the standard form of the equation of the circle with the given center and radius. $$\text { Center }(-3,5), r=3$$

Step-by-Step Solution

Answer

The standard form of the equation of the circle is \((x + 3)^2 + (y - 5)^2 = 9\).

Step 1: Identify the given values

Here, the center of the circle \((h, k)\) is \((-3, 5)\) and the radius \(r\) is \(3\). Thus, \(h = -3\), \(k = 5\), and \(r = 3\).

Step 2: Plug values into the standard form

Substitute the given values into the standard form equation of a circle. This gives us: \((x - (-3))^2 + (y - 5)^2 = 3^2\).

Step 3: Simplify the equation

Finally, simplify the equation to its standard form. Note that subtracting a negative number turns it into addition. Hence, the equation becomes: \((x + 3)^2 + (y - 5)^2 = 9\).