Question

Which translation results in a circle whose center is at the origin? Question 5 options: Circle open parentheses x plus 2 close parentheses squared plus open parentheses y minus 6 close parentheses squared equals 4 translated 2 units right and 6 units down. Circle open parentheses x minus 1 close parentheses squared plus open parentheses y plus 2 close parentheses squared equals 4 translated 1 unit left and 2 units down. Circle open parentheses x minus 2 close parentheses squared plus open parentheses y plus 3 close parentheses squared equals 4 translated 2 units right and 3 units up. Circle open parentheses x minus 3 close parentheses squared plus open parentheses y minus 5 close parentheses squared equals 4 translated 3 units left and 5 units up.

Answer 1

Answer:

case 1) Circle open parentheses x plus 2 close parentheses squared plus open parentheses y minus 6 close parentheses squared equals 4 translated 2 units right and 6 units down

Step-by-step explanation:

Verify the 4 Options

case 1) Circle open parentheses x plus 2 close parentheses squared plus open parentheses y minus 6 close parentheses squared equals 4 translated 2 units right and 6 units down

The equation of the circle is

$(x+2)^{2}+(y-6)^{2}=4$

The center of the circle is the point $(-2,6)$

The rule of the translation is

$(x,y)-------> (x+2,y-6)$

Applying the rule to the center

$(-2,6)-------> (-2+2,6-6)$

$(-2,6)-------> (0,0)$

Therefore

The translation results in a circle whose center is at the origin

case 2) Circle open parentheses x minus 1 close parentheses squared plus open parentheses y plus 2 close parentheses squared equals 4 translated 1 unit left and 2 units down

The equation of the circle is

$(x-1)^{2}+(y+2)^{2}=4$

The center of the circle is the point $(1,-2)$

The rule of the translation is

$(x,y)-------> (x-1,y-2)$

Applying the rule to the center

$(1,-2)-------> (1-1,-2-2)$

$(1,-2)-------> (0,-4)$

Therefore

The translation results in a circle whose center is not at the origin

case 3) Circle open parentheses x minus 2 close parentheses squared plus open parentheses y plus 3 close parentheses squared equals 4 translated 2 units right and 3 units up

The equation of the circle is

$(x-2)^{2}+(y+3)^{2}=4$

The center of the circle is the point $(2,-3)$

The rule of the translation is

$(x,y)-------> (x+2,y+3)$

Applying the rule to the center

$(2,-3)-------> (2+2,-3+3)$

$(2,-3)-------> (4,0)$

Therefore

The translation results in a circle whose center is not at the origin

case 4) Circle open parentheses x minus 3 close parentheses squared plus open parentheses y minus 5 close parentheses squared equals 4 translated 3 units left and 5 units up

The equation of the circle is

$(x-3)^{2}+(y-5)^{2}=4$

The center of the circle is the point $(3,5)$

The rule of the translation is

$(x,y)-------> (x-3,y+5)$

Applying the rule to the center

$(3,5)-------> (3-3,5+5)$

$(3,5)-------> (0,10)$

Therefore

The translation results in a circle whose center is not at the origin