Conic Sections Algebra II

Parabola Horizontal Formula

x=a(y-k)²+h

Parabola Vertical Formula

y=a(x-h)²+k

Circle Formula (centered at origin)

x²+y²=r²

Circle Formula - centered at a point (h,k)

(x-h)²+(y-k)²=r²

Ellipse Horizontal Formula (centered around origin) where a²>b²

x²/a²+y²/b²=1

Ellipse Vertical Formula (centered around origin) where a²>b²

x²/b²+y²/a²=1

Ellipse Horizontal Formula - centered around (h,k) where a²>b²

(x-h)²/a²+(y-k)²/b²=1

Ellipse Vertical Formula - centered around (h,k) where a²>b²

(x-h)²/b²+(y-k)²/a²=1

Hyperbola Horizontal Formula (centered at the origin)

x²/a²-y²/b²=1

Hyperbola Vertical Formula (centered at the origin)

y²/a²-x²/b²=1

Hyperbola Horizontal Formula - centered at point (h,k)

(x-h)²/a²-(y-k)²/b²=1

Hyperbola Vertical Formula - centered at point (h,k)

(y-k)²/a²-(x-h)²/b²=1

General Form For Parabola (both)

x=ay²+by+c and y=ax²+bx+c

General Form - For everything else

Ax²+By²+Cx+Dy+E=0 remember it’s a 0 on the end