1. Problem 21: Find the equation of the circle with center at (2, 3) and radius 5. The general form of a circle's equation is $$ (x - h)^2 + (y - k)^2 = r^2 $$ where $ (h, k) $ is the center and $ r $ is the radius. Here, $ h = 2 $, $ k = 3 $, $ r = 5 $. So, $$ (x - 2)^2 + (y - 3)^2 = 5^2 = 25 $$ Match with options: Option D. 2. Problem 22: Find the equation of a circle with center at origin (0,0) and diameter 8. Radius $ r = \frac{\text{diameter}}{2} = \frac{8}{2} = 4 $. Equation: $$ x^2 + y^2 = r^2 = 4^2 = 16 $$ Match with options: Option C. 3. Problem 23: Equation of circle with center at (0, -8) and radius $ \sqrt{2} $. Equation form: $$ (x - 0)^2 + (y - (-8))^2 = (\sqrt{2})^2 $$ which is $$ x^2 + (y + 8)^2 = 2 $$ Match with options: Option B. 4. Problem 24: Given equation $$ (x + 1)^2 + (y - 1)^2 = 5 $$, find the quadrant of center. Center is at $ (-1, 1) $. $x = -1 < 0$, $y = 1 > 0$, so center lies in Quadrant II. Match with options: Option B. 5. Problem 25: Given $$ x^2 + y^2 = 1 $$, identify which is TRUE. This is a circle with center at origin $(0,0)$ and radius $1$. So, correct is "Its center lies on the origin". Match with options: Option A. Final answers: 21: D 22: C 23: B 24: B 25: A