Question

What is the equation for the translation of x2 + y2 = 16 seven units to the right and five units up?

Answer 1

Answer:

$(x-7)^2+(y-5)^2=16$.

Step-by-step explanation:

The given circle has equation $x^2+y^2=16$.

This is the equation that has its center at the origin with radius 4 units.

When this circle is translated seven units to the right and five units up, then the center of the circle will now be at (7,5).

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

This implies that, the translated circle will now have equation.

$(x-7)^2+(y-5)^2=4^2$.

$(x-7)^2+(y-5)^2=16$.