Question

1. -/1 points write the standard form of the equation of the circle with the given characteristics. center: (0, 0); radius: 7

Explanation:

Step1: Recall the standard 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

Given center \((h, k) = (0, 0)\) and radius \(r = 7\). Substitute \(h = 0\), \(k = 0\), and \(r = 7\) into the formula: \((x - 0)^2 + (y - 0)^2 = 7^2\).

Step3: Simplify the equation

Simplify \((x - 0)^2\) to \(x^2\), \((y - 0)^2\) to \(y^2\), and \(7^2\) to \(49\). So the equation becomes \(x^2 + y^2 = 49\).

Answer:

\(x^2 + y^2 = 49\)