Question

Complete the following: 1. Find the equation of the circle having the given center and radius. (a) C(0, 0), r= 3 (b) C(-2,-5), r=4 (c) C(4, 3), r= 5 (d) C(2,-3), r= 6

Answer 1

Circle equation:

$(x-h)^2+(y-k)^2=r^2$

where (h, k) is the center of the circle and r is its radius.

c) Replacing with center at (4,3) and r = 5, we get:

$\begin{gathered} (x-4)^2+(y-3)^2=5^2 \\ (x-4)^2+(y-3)^2=25 \end{gathered}$

d) Replacing with center at (2,-3) and r = 6, we get:

$\begin{gathered} (x-2)^2+(y-(-3))^2=6^2 \\ (x-2)^2+(y+3)^2=36 \end{gathered}$

a) Replacing with center at (0,0) and r = 3, we get:

$\begin{gathered} (x-0)^2+(y-0)^2=3^2 \\ x^2+y^2=9 \end{gathered}$

b) Replacing with center at (-2,-5) and r = 4, we get:

$\begin{gathered} (x-(-2))^2+(y-(-5))^2=4^2 \\ (x+2)^2+(y+5)^2=16 \end{gathered}$