another practice geometry ?n please help?

Question

What is the equation of a circle with center C(1, -1) and a point on the circle P(-2, 1)?


A.
(x - 1)2 + (y + 1)2 = 169

B.
(x + 1)2 + (y - 1)2 = 169

C.
(x + 2)2 + (y - 1)2 = 13

D.
(x - 1)2 + (y + 1)2 = 13

Answer 1

(x-x0)^2+(y-y0)^2=r^2
C(x0, y0)
so C(1,-1)=>x0=1, y0=-1
and P(-2,1)on circle=>
(-2-1)^2+(1-(-1))^2=9+4=13=r^2
so the equation is
(x-1)^2+(y+1)^2=13 the answer is D

Answer 2

The distance between the center and a point on the circle is the radius.

CP = SQRT(3^2 + 2^2)
CP = SQRT(13)

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

The equation for the circle is (x - 1)^2 + (y + 1)^2 = 13

Answer 3

(x-1)² + (y+1)² = 13. distance between the points, √13, is the radius.

Answer 4

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