Question

Write an equation for the translation of x^2+y^2=49 by 3 units left and 4 units up

Answer 1

The answer is:

$(x+3)^2+(y-4)^2=49$

Answer 2

$\bf \textit{equation of a circle}\\\\ (x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2 \qquad \begin{array}{lllll} center\ (&{{ h}},&{{ k}})\qquad radius=&{{ r}} \end{array}\\\\ -----------------------------\\\\ x^2+y^2=49\iff (x-0)^2+(y-0)^2=7^2\quad \begin{cases} h=0\\ k=0 \end{cases} \\\\\\ (x-\underline{(-3)})^2+(y-\underline{(+4)})^2=7^2\quad \begin{cases} h=-3\\ k=4 \end{cases} \\\\\\ \boxed{(x+3)^2+(y-4)^2=49}$