Question

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

(x + 7)2 + (y + 5)2 = 16

(x − 7)2 + (y − 5)2 = 16

(x + 7)2 + (y − 5)2 = 16

(x − 7)2 + (y + 5)2 = 16

Answer 1

• (x − 7)2 + (y − 5)2 = 16

Explanation:

The given circle has equation

`\sf \: x^2+y^2=16x`

The equation of a circle with center (h,k) and radius r units is

`\sf(x-h)^2+(y-k)^2=r^2(x−h)`

`\sf(x-7)^2+(y-5)^2=4^2(x−7)`

`\sf(x-7)^2+(y-5)^2=16(x−7)`

❖ Tip❖ :-

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).