A conic section has the equation x2 + y2 + 12x + 8y = 48. Determine the following: type of conic, domain and range, axes of symmetry, and center. Show your work.

Question

anonymous · Answer

So I know it is a circle with the equation (x+6)^2+(y+4)^2=10^2
I'm pretty sure that it has infinite axis of symmetry since it is a circle, right?
How do I find domain and range and center?

anonymous · Answer

@Mertsj

mertsj · Answer

Write it in this form:
$$(x-h)^2+(y-k)^2=r^2$$

anonymous · Answer

Ya I did (x+6)^2+(y+4)^2=10^2 :P

mertsj · Answer

The center of that circle is (h,k) and the radius is r

anonymous · Answer

So center is (6,4)

mertsj · Answer

(x-(-6))^2+(y-(-4))^2=10^2

anonymous · Answer

Ohh I see, (-6,-4)

mertsj · Answer

yes

anonymous · Answer

Domain and range? and axis of symmetry?

mertsj · Answer

Now the domain:  If the center is (-6,-4) and the radius is 10, what x values would be on the circle?

anonymous · Answer

-16 to 4?

mertsj · Answer

Exactly.

anonymous · Answer

So domain is -16<x<4?

mertsj · Answer

So domain is [-16.4] in interval notation

mertsj · Answer

yes

mertsj · Answer

And apply the same thought process for the range.

anonymous · Answer

And range -14<y<6?

mertsj · Answer

yes

anonymous · Answer

And just to check, for the axis of symmetry, I would but infinite?

mertsj · Answer

Does it want to know how many axes of symmetry?

anonymous · Answer

No, it wants to know what the axis of symmetry is

mertsj · Answer

That is a weird question.  Any line through the center is an axis of symmetry

mertsj · Answer

So do you have answer choices?

anonymous · Answer

I think I'll just put "all lines through center axis".. and no, no choices on this one

mertsj · Answer

That sounds right.  You might say, "Any line that contains (-6,-4) is an axis of symmetry and so there is an infinite number of axes of symmetry."

anonymous · Answer

Thanks for the 100th time haha, you're an amazing helper!

mertsj · Answer

yw,  my pleasure to work with such a smart fellow.