Question

1)Find the center & radius for the following

1. 2x^2+2y^2=72
2. (x-3)^2+(y-1)^2=4
3. (x-5)^2+(y+2)^2=49
4. (y-4)^2+(x-10)^2=64
5.(x^2-6x+9)+(y^2+8y+16)=1
6. x^2+12x+y^2-8y=-27
7. Write an equation for the circle with center at (3,-4) and with (2,-1) a point on the circle.

Answer 1

The general equation of circles is (x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center.
1. 2x^2+2y^2=72 =x^2+y^2=36 c: (0,0); r = 6
2. (x-3)^2+(y-1)^2=4 : c: (3,1); r = 2
3. (x-5)^2+(y+2)^2=49; c: (5,-2); r = 7
4. (y-4)^2+(x-10)^2=64: c: (4,10); r = 8
5.(x^2-6x+9)+(y^2+8y+16)=1: c: (3,-4); r = 1
6. x^2+12x+y^2-8y=-27 =x^2+12x + 36+y^2-8y+16=-27+36+16=25:
c( -6,4); r = 5