conic sections Flashcards
x and y squared , same coefficient / sign
Circle
only one variable is squared
Parabola
x and y squared , BOTH POSITIVE
Ellipse
x and y squared , 1 POSITIVE 1 NEGATIVE
Hyperbola
Equation of Circle
(x-h)² + (y-k)² = r²
Horizontal Parabola
(x-h)² = 4p (y-k)
Vertical Parabola
4p (x-h) = (y-k)²
Latus rectum
4p , 2p each from focus
PARABOLA:
4p is at (y-k) ; p > 0
UP
PARABOLA:
4p is at (y-k) ; p < 0
DOWN
PARABOLA:
4p is at (x-h) ; p > 0
RIGHT
PARABOLA:
4p is at (x-h) ; p < 0
LEFT
Horizontal Ellipse
(x-h)² / a² + (y-k)² / b² = 1
Vertical Ellipse
(x-h)² / b² + (y-k)² / a² = 1
Ellipse (a)
Center to Vertex
Ellipse (b)
Center to Minor Axis
Ellipse (c)
Center to Focus
Ellipse :
Bigger denominator at x
Horizontal
Ellipse :
Bigger denominator at y
Vertical
Horizontal Hyperbola
(x-h)² / a² - (y-k)² / b² = 1
Vertical Hyperbola
(y-k)² / a² + (x-h)² / b² = 1
Hyperbola :
Positive is at x
Horizontal
Hyperbola :
Positive is at y
Vertical