Match the following equations with the conic sections formed by them. 1. x 2 + y 2 - 4x + 6y - 5 = 0 hyperbola 2. x 2 - 6y = 0 circle 3. 4x 2 + 9y 2 = 1 ellipse 4. 7x 2 - 9y 2 = 343 parabola

1. circle
 2. parabola
 3. ellipse
 4. hyperbola
   Let's look at each equation and see what they are:
   1. x^2 + y^2 - 4x + 6y - 5 = 0
 * There's a lot of crud in this equation, but the thing to note is that the x^2 and y^2 terms have the same scaling factor (which is 1). This should scream "circle" to you.

   2. x^2 - 6y = 0
 * Key thing to note here is that the y term isn't squared, but the x term is squared. This is a key sign that the equation is a parabola.

   3. 4x^2 + 9y^2 = 1
 * Here we have the sum of an x squared term and a y squared term. That kinda sounds like a circle, but there's those 2 coefficients scaling the results. And they're different. So we're looking for a closed curve that kinda looks like a circle, but it's stretched out a bit. And that's an ellipse.

   4. 7x^2 - 9y^2 = 343
* Here we have a couple of squared terms for x and y. But we're not adding them together, we're subtracting. And that indicates a hyperbola.