✨ Conic Sections Explorer ✨
Discover the magic of curves in mathematics!
1 Identify the conic section:
2x² - y² = 7
Step 1: Look at the equation form
The equation has both x² and y² terms with different coefficients.
Step 2: Check the signs
The x² term is positive (2x²) and y² term is negative (-y²).
Step 3: Determine the type
When x² and y² have opposite signs, it's a hyperbola!
HYPERBOLA
2 Identify the conic section:
3x² + 3y² - 4x + 3y + 10 = 0
Step 1: Look at the equation form
The equation has both x² and y² terms with the same coefficients (both 3).
Step 2: Check the signs
Both squared terms are positive.
Step 3: Determine the type
When x² and y² have same coefficients and same signs, it's a circle!
CIRCLE
3 Identify the conic section:
3x² + 2y² = 14
Step 1: Look at the equation form
The equation has both x² and y² terms with different coefficients.
Step 2: Check the signs
Both squared terms are positive.
Step 3: Determine the type
When x² and y² have same signs but different coefficients, it's an ellipse!
ELLIPSE
4 Identify the conic section:
x² + y² + x - y = 0
Step 1: Look at the equation form
The equation has both x² and y² terms with the same coefficients (both 1).
Step 2: Check the signs
Both squared terms are positive.
Step 3: Determine the type
When x² and y² have same coefficients and same signs, it's a circle!
CIRCLE
5 Identify the conic section:
11x² - 25y² - 44x + 50y - 256 = 0
Step 1: Look at the equation form
The equation has both x² and y² terms with different coefficients.
Step 2: Check the signs
The x² term is positive (11x²) and y² term is negative (-25y²).
Step 3: Determine the type
When x² and y² have opposite signs, it's a hyperbola!
HYPERBOLA
6 Identify the conic section:
y² + 4x + 3y + 4 = 0
Step 1: Look at the equation form
The equation has only one squared term (y²) and a linear x term.
Step 2: Check the pattern
When only one variable is squared, it's usually a parabola.
Step 3: Determine the type
This is a parabola that opens sideways!
PARABOLA