<span>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.</span>
We assume the 140 refers to the number animals (heads, noses, bodies, whatever). If all of those were chickens, there would be 280 legs. There are 160 legs more than that.
Since each pig that replaces a chicken adds 2 legs, there must be 160/2 = 80 pigs. That leaves 140 -80 = 60 chickens.
