How do you find the equation of the circle that is shifted 5 units to the left and 2 units down from the circle with the equation x^2+y^2=19?

1 Answer
Nov 17, 2015

Answer:

Its equation may be written:

#(x+5)^2+(y+2)^2 = 19#

Explanation:

The centre of the original circle is #(0, 0)#. The centre for our shifted circle is #(-5, -2)#.

Just replace #x# with #x+5# and #y# with #y+2# in the original equation to get:

#(x+5)^2+(y+2)^2 = 19#

In fact if #f(x, y) = 0# is the equation of any curve, then #f(x+5, y+2) = 0# is the equation of the same curve shifted left #5# units and down #2# units.