Conics (copy)

Equation of a Circle

(x-h)²+(y-h)² = r²

Equation of Ellipse

(x-h)²/a² + (y-k)²/b² = 1

Foci of Ellipse

c²=a²-b²

Major Axis Foci along y int

(h,k±c)

Major Axis Foci along x int

(h±c,k)

Major Axis or Major Radius

MA=2a

Minor Axis or Minor Radius

MinA=2b

Vertical Hyperbola Equation

(y-k)²/a² - (x-h)²/b² = 1

Horizontal Hyperbola Equation

Standard form: (x-h)²/a² - (y-k)²/b² = 1

Hyperbola Foci

c²=a²+b²

Vertical Hyperbola Foci

(h,k±c)

Horizontal Hyperbola Foci

(h±c,k)

Vertical Hyperbola Asymptotes

y-k=±a/b(x-h)

Parable opens right

(y-k)²=+4p(x-h)

Parable opens left

(y-k)²=-4p(x-h)

Parable opens up

(x-h)²=+4p(y-k)

Parable opens down

(x-h)²=-4p(y-k)

Foci for Parable opens down/up

(h,k+c)

Foci for Parable opens left/right

(h+c,k)

Horizontal Hyperbola Asymptotes

y-k=±b/a(x-h)

Vertical Directrix

y= k±a²/c

Horizontal Directrix

x= h±a²/c

Horizontal Co-vertices

(h, k±b)

Vertical Co-vertices

(h±b,k)

Elipse Focal Distance

c² = a²-b²