Question

A conic section has the equation x^2 + y^2 + 12x + 8y = 48. Determine the following: type of conic, domain and range, axes of symmetry, and center.

I really need help with this, I'm absolutely horrid with conic sections.

Answer 1

Let's see if this helps:
1. Parabola: x^1 y^2 or y^1 x^2
2. Circle: x^2 & y^2 signs and coefficients the same
3. Ellipse: x^2 & y&2 both positive, coefficients different
4. Hyperbola: x^2 and y^2...one positive and one negative

Answer 2

@Mertsj So it's a circle? I still don't really get it... sorry.

Answer 3

yes. it is a circle. Good job.

Answer 4

@Mertsj I still don't understand the rest of it, how do I find a, b, and c?

Answer 5

Now that we have identified it as a circle, we have to put it in the right form. This is the right form:
\[(x-h)^2+(y-k)^2=r^2\]

Answer 6

Does that look familiar?

Answer 7

@Mertsj So it would be this?
(x - sqrt(12))^2 + (y - sqrt(8))^2

Answer 8

So we should take x^2 + 12x and complete the square. Can you do that?

Answer 9

Ah, that's another thing I suck at, unfortunately. I can try searching it up though.

Answer 10

Take half of 12 which is 6. Square that. 6 squared is 36. Add 36 to both sides of the equation.

Answer 11

Now take the y^2 + 8y and do the same thing.

Answer 12

So now it's this?

(x^2 + 12x + 36) + (y^2 + 8x + 16) = 48?