2 geometry ?n's can any one answer!?

Question

Which translation results in a circle whose center is at the origin?


A.
Circle (x + 2)^2 + (y - 6)^2 = 4 translated 2 units right and 6 units down.

B.
Circle (x - 1)^2 + (y + 2)^2 = 4 translated 1 unit left and 2 units down.

C.
Circle (x - 2)^2 + (y + 3)^2 = 4 translated 2 units right and 3 units up.

D.
Circle (x - 3)^2 + (y - 5)^2 = 4 translated 3 units left and 5 units up.


Which equation represents the image of circle (x - 5)^2 + (y + 12)^2 = 169 after a translation 2 units right and 3 units down?


A.
(x - 7)^2 + (y + 15)^2 = 169

B.
(x - 3)^2 + (y + 9)^2 = 169

C.
(x+ 7)^2 + (y - 15)^2 = 169

D.
(x+ 3)^2 + (y - 9)^2 = 169

Answer 1

Hello

The equation used is the standard equation that has the form


(x - h)2 + (y - k)2 = r2

where h and k are the x- and y-coordinates of the center of the circle and r is the radius.

Thus a circle with an equation of (x + 2)^2 + (y - 6)^2 = 4 has its center at -2, 6 and the radius is 2.

Thus:
Which translation results in a circle whose center is at the origin?

A.
Circle (x + 2)^2 + (y - 6)^2 = 4 translated 2 units right and 6 units down. ------- THIS IS THE ANSWER. Its center is at -2,6. Thus shifting 2 units to right and 6 down will have its center at 0,0.

B.
Circle (x - 1)^2 + (y + 2)^2 = 4 translated 1 unit left and 2 units down. WRONG: Center is at 1,-2. This translation will place its center at 0,-4.

C.
Circle (x - 2)^2 + (y + 3)^2 = 4 translated 2 units right and 3 units up. WRONG: Center is at 2,-3. This translation will place its center at 4,0.


D.
Circle (x - 3)^2 + (y - 5)^2 = 4 translated 3 units left and 5 units up. WRONG: Center is at 3,5. This translation will place its center at 0,10..

Also,
Which equation represents the image of circle (x - 5)^2 + (y + 12)^2 = 169 after a translation 2 units right and 3 units down?

The center is at 5,-12 with a radius of 13. Thus translated 2 units right and 3 units down --- the center will be at 7, -15. This is option C. (x+ 7)^2 + (y - 15)^2 = 169

A.
(x - 7)^2 + (y + 15)^2 = 169

B.
(x - 3)^2 + (y + 9)^2 = 169

C.
(x+ 7)^2 + (y - 15)^2 = 169

D.
(x+ 3)^2 + (y - 9)^2 = 169

Hope this helps

Answer 2

A because the original circle has its center at (-2,+6)

C because the original circle's center is at (5,-12),

Answer 3

C
B