# 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?

Nov 17, 2015

Its equation may be written:

${\left(x + 5\right)}^{2} + {\left(y + 2\right)}^{2} = 19$

#### Explanation:

The centre of the original circle is $\left(0 , 0\right)$. The centre for our shifted circle is $\left(- 5 , - 2\right)$.

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

${\left(x + 5\right)}^{2} + {\left(y + 2\right)}^{2} = 19$

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