# Difference between revisions of "005 Sample Final A, Question 16"

Question Graph the following,

${\displaystyle -x^{2}+4y^{2}-2x-16y+11=0}$
Foundations:
1) What type of function is this?
2) What can you say about the orientation of the graph?
1) Since both x and y are squared it must be a hyperbola or an ellipse. We can conclude that the graph is an ellipse since both ${\displaystyle x^{2}}$   and   ${\displaystyle y^{2}}$ have the same sign, positive.
2) Since the coefficient of the ${\displaystyle x^{2}}$ term is smaller, when we divide both sides by 36 the X-axis will be the major axis.
We start by dividing both sides by 36. This yields ${\displaystyle {\frac {4x^{2}}{36}}+{\frac {9(y+1)^{2}}{36}}={\frac {x^{2}}{9}}+{\frac {(y+1)^{2}}{4}}=1}$.
The four vertices are: ${\displaystyle (-3,-1),(3,-1),(0,1){\text{ and }}(0,-3)}$