Question

The graph of the equation x2 + y2 + 8x − 10y − 40 = 0 is which of the following conic sections?

ellipse

hyperbola

parabola

circle

Answer 1

in form
ax^2+by^2+cx+dy+e=0
to determine the shape
when a=c and b=d, you have a circle

if you do b^2-4ac
if:
1. the result is GREATER than zero: hyperbola
2. result is EQUAL to zero: parabola
3. result is LESS than zero: elipse




x^2+y^2+8x-10y-40
a is not equal c so nt circle
a=1
b=1
c=8
1^2-4(1)(8)
we can see this is less than 0
ellipse