The document discusses circle equations with a given center point and radius. It provides the general equation for finding the distance between two points and uses this to derive the equation of a circle given its center P(-2,3) and passing through point Q(4,-1). It then shows the equations for circles with this center that meet exactly one point X and one point Y.

1. MATH TASK GROUP 1 DIAN PERMANA ANNISA INDAH REZA DHIA ATIKAH ALIYYU USWATUN HASANAH WAN ELSA

2. The Circle Equation with Center P(a,b) and radius r ! The general equation distance is : (x2-x1)2 + (y2-y1)2 =r2 So in the circle, x1 = a y1 = b x2 = x y2 = y Then the circle equation become : (x-a)2 + (y-b)2= r2 y T(x,y) r P(a,b) x

3. Example . . . Determine the circle equation with center P(-2,3) with the following requirement : a. Passing through point Q(4,-1) b. Meet an exatly one point X c. Meet an exatly one point Y

4. Answers . . . 1. a. Q(4,-1) P(2,-3) (4-2)2 +(-3+1)2 = r2 (2)2 + (-2)2 = r2 8 = r2 (x-2)2 + (y+1)2 = 8 b. Meet an exatly one point X means r = b = 3 (x-2) + (y+1) = 9 c. Meet an exatly one point Y means r = a = 2 (x-2) + (y+1) = 4