How do you write an equation for the translation of x^2 + y^2 = 25 by 7 units left and 2 units down?

1 Answer
Oct 17, 2016

Answer:

The equation of the translated circle is:
#(x + 7)^2 + (y + 2)^2 = 25#.

Explanation:

The standard form of a circle is
#(x -h)^2 + (y - k)^2 = r^2#,
where #r# is the radius of the circle and #(h, k)# is the center of the circle.

In #x^2 + y^2 = 25#, the center is at #(0, 0)#. When the circle is translated left 7 units, it means that the new center has #h = -7#. Translating the circle down 2 units means that the new center has #k = -2#. So, the translated circle has the equation

#(x + 7)^2 + (y + 2)^2 = 25#.