For the conic section with the equation

Question

X²+ 10x+y²-14y+64=0

what is true 

a. The gragh is a parabola with its vertex at (-5,7)

b.the graph is an ellipse with its vertices at (-5,-1) and (-5,15)

c.the graph has a focus at (-5/2,7)

d. The graph is a circle with its center at (-5,7)

Answer 1

There are squared terms for both x and y, and they both have the same sign.  That means that the curve must be a circle or an elipse.  (A parabola only has a squared term for one of the variables, and a hyperbola has squared terms for both but they have opposite signs).

 

Also, the coefficients of x² and y² are the same (both 1), so the curve must be a circle.

 

So that eliminates a and b.

 

In addition, a circle does not have a focus, so that eliminates c.  The only possible answer is d.