Parabola Flashcards
e value of parabola
e=1, h^2=ab
Standard Parabola
y^2=4ax
Axis of parabola
Line passing through focus and perpendicular to the directrix
Vertex
Point of intersection of parabola and axis
Foot of directrix
Point of intersection of directrix and axis
Double ordinate
Chord of the parabola perpendicular to the axis
Focal Chord
Chord of the parabola passing through the focus
Latus Rectum
Double ordinate passing through focus
Focal chord perpendicular to the axis
Ends of LR
(a, ±2a)
Length of LR
4a
Parametric Coordinates
at^2, 2at
Chord Equation
2x - (t1+t2)y + 2at1t2
If it is a focal chord, then what is the conditions on parametric coordinates?
t1t2=-1
Length of focal chord
a(t+1/t)^2
Conditions of tangency of parabola
c=a/m
Point Form Tangent equation
yy1=2a(x+x1)
Slope Form Tangent equation
y = mx+a/m
Parametric Form Tangent equation
yt = x+at^2
POI of tangents at t1 and t2
at1t2, a(t1+t2)
Point Form of Normal
y-y1=-y1/2a(x-x1)
Parametric Form of Normal
y +xt = 2at + at^3
Slope Form of Normal
y=mx-2am-am^3
Director circle for a parabola
Directrix
Conditions of normality
c = -2am-am^3
POI of normals at t1 and t2
a(t1^2+t2^2+t1t2+2), -at1t2(t1+t2)
If the normal at t1 meets the parabola again at t2, then the relation
t2=-t1-2/t1
Equation of normal from any point
am^3+m(2a-h)+k=0
Co-normal points
Foot of the normals of three concurrent normals
Sum of ordinates of three co-normal point is
0
