Question

1. a circle in the xy - plane has center (1,3) and radius 4. which of the following is an equation of the circle? (a) (x - 1)^2+(y - 3)^2 = 4 (b) (x + 1)^2+(y + 3)^2 = 4 (c) (x - 1)^2+(y - 3)^2 = 16 (d) (x + 1)^2+(y + 3)^2 = 16 2. a circle in the xy - plane has center (4, - 6) and radius 3. which of the following is an equation of the circle?

Explanation:

Step1: Recall the standard form of a circle equation

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

Step2: Substitute the given center and radius into the formula

Given center \((1,3)\) (so \(h = 1,k = 3\)) and radius \(r = 4\). Substitute into the formula: \((x - 1)^2+(y - 3)^2=4^2\).

Step3: Calculate \(r^2\)

Since \(r = 4\), \(r^2=16\). So the equation is \((x - 1)^2+(y - 3)^2=16\).

Answer:

C. \((x - 1)^2+(y - 3)^2=16\)