Answer
It's an ellipse
Work Step by Step
Standard from : $\frac{(x-p)^2}{a^2}+\frac{(y-q)^2}{b^2}$
$\frac{(x-1)^2}{49}+\frac{(y+2)^2}{25}=1$
From the standard equation, centre =$(p,q)$,
$(1,-2)$
foci: $c^2=a^2-b^2$ and foci are at $(p+/-c;q)$
$(1-2\sqrt 6;-2)$ and $(1-2\sqrt 6;-2)$
The graph is shown below
