Question

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?

Answer 1

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.