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.

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

The center of the circle is the point

The rule of the translation is

Applying the rule to the center

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

The center of the circle is the point

The rule of the translation is

Applying the rule to the center

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

The center of the circle is the point

The rule of the translation is

Applying the rule to the center

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

The center of the circle is the point

The rule of the translation is

Applying the rule to the center

Therefore

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