First Question of My Algebra Review

Question

1.

a. Find an equation of the circle which contains the origin and has the center (3,-4).

b. Find the radius and center of the circle given by (x+3)^2+y^2=81.

c. Find an equation of the circle with endpoints of diameter (8,-2) and (-4,4).

Answer 1

a circle equation has r^2 = 9+16 =25

the equation is (x-3)^2 + (y+4)^2 = 25

b (x+3)^2 + y^2 =81 has center (-3,0) and radius sqr81 = 9

c endpoints (8,-2) and (-4,4) have center that's their midpoint (2,1) The midpoint has x coordinate that's the average of 8 and -4, with y coordinate that's the average of -2 and 4.

general equation for a circle is (x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r=radius

with Center (2,1)

that equation is (x-2)^2 + (y-1)^2 = r^2

plug in either point to solve for the radius =r

(8-2)^2 + (-2-1)^2 = r^2

36 +9 = 45 = r^2

the circle's equation is:

(x-2)^2 + (y-1)^2 = 45