List of formulas related to Analytic-geometry (Conic Sections)
The Parabola Formulas:
The standard formula of a parabola y2=2px Parametric equations of the parabola:
x=2pt2y=2ptTangent line in a point D(x0,y0) of a parabola y2=2px is :
y0y=p(x+x0)Tangent line with a given slope m:
y=mx+p2mTangent lines from a given point. Take a fixed point P(x0,y0). The equations of the tangent lines are:
y−y0=m1(x−x0)y−y0=m2(x−x0)m1=y0+√y20−2px02x0m2=y0−√y20−2px02x0The Ellipse Formulas:
The set of all points in the plane, the sum of whose distances from two fixed points, called the foci, is a constant.
The standard formula of a ellipse:
x2a2+y2b2=1Parametric equations of the ellipse:
x=acosty=bsintTangent line in a point D(x0,y0) of a ellipse:
x0xa2+y0yb2=1Eccentricity of the ellipse:
e=√a2−b2aFoci of the ellipse:
if a≥b⟹F1(−√a2−b2,0) F2(√a2−b2,0)if a<b⟹F1(0,−√b2−a2) F2(0,√b2−a2)Area of the ellipse:
A=π⋅a⋅bThe Hyperbola Formulas:
The set of all points in the plane, the difference of whose distances from two fixed points, called the foci, remains constant.
The standard formula of a hyperbola:
x2a2−y2b2=1Parametric equations of the Hyperbola:
x=asinty=bsintcostTangent line in a point D(x0,y0) of a Hyperbola:
x0xa2−y0yb2=1Foci:
if a≥b⟹F1(−√a2+b2,0) F2(√a2+b2,0)if a<b⟹F1(0,−√a2+b2) F2(0,√a2+b2)Asymptotes:
if a≥b⟹y=bax and y=−baxif a<b⟹y=abx and y=−abx