Question

give the equation for the new circle obtained by translating the circle (x-2)^2+(y+4)^2=36 by 6 units to the right and 4 units up explain and show your work please

Answer 1

equation for the new circle is;

(x - 8)² + y² = 36

Explanation:

There are two types of translations and they are translation horizontally and vertically. Combining both of them in the context of this question, to translate a circle 6 units to the right and 4 units up, we take our equation,

(x - 2)² + (y + 4)² = 36 and subtract 6 from the x - term and 4 from the y - term to get the equation of the new circle.

This gives us;

(x - 2 - 6)² + (y + 4 - 4)² = 36

This gives;

(x - 8)² + y² = 36