Identifying circles parabolas ellipses or hyperbolas?

Question

9x² - 9y² = 36

4x²-9y=36

4x-9y²=36

4x²-9y²=36

9x²+9y²=36

what are these? graphic calculator doesnt work

Answer 1

For a very rough guide just for identifying when you have to decide between circle, ellipse, hyperbola, or parabola. I'm not showing the coefficients, it's just the pattern to look for.

x² + y² = 1 = circle if the coefficients are the same, ellipse if they're not

x² - y² = 1 = hyperbola

x² - y = 1 = parabola

Answer 2

If only one of the variables is squared, it's a parabola.

If the two terms have different signs, it's a hyperbola.

If the two terms have the same sign, it's an ellipse.

Answer 3

9x² - 9y² = 36  hyperbola

4x²-9y=36  parabola

4x-9y²=36 parabola

4x²-9y²=36 hyperbola

9x²+9y²=36 circle.

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