Questions: Find the equation of the circle with a center at (-3,5) and a radius of 6.7.

Solution Steps

To find the equation of a circle given its center and radius, we use the standard form of the circle's equation: \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius. Here, the center is \((-3, 5)\) and the radius is \(6.7\).

1. Substitute the center \((-3, 5)\) into \((h, k)\).
2. Substitute the radius \(6.7\) into \(r\).
3. Calculate \(r^2\).
4. Form the equation using the standard form.

The center of the circle is given as \((-3, 5)\) and the radius is \(6.7\).

The standard form of the equation of a circle is: \[ (x - h)^2 + (y - k)^2 = r^2 \] Substituting \(h = -3\), \(k = 5\), and \(r = 6.7\) into the equation, we get: \[ (x - (-3))^2 + (y - 5)^2 = 6.7^2 \]

Simplify the terms inside the parentheses and calculate \(r^2\): \[ (x + 3)^2 + (y - 5)^2 = 6.7^2 \] \[ 6.7^2 = 44.89 \] Thus, the equation becomes: \[ (x + 3)^2 + (y - 5)^2 = 44.89 \]

Final Answer