एक दन COORDINATE IN
JEE 2022 COMPLETE REVISION
Lecture-3
Parabola
Short notes
Standard Parabolas and
Important Terminologies
Important Relations
Position of Point
Position of Line
4acosec2𝜶
Intersecting :
Tangent :
Non
Intersecting :
Length of
Intercept:
Equation of Tangent
Intersection of Tangents
Equation of Normal
For y2 = 4ax
1. Point form:
2. Parametric form:
3. Slope form:
Important Relations: Normals
Important Relations: Normals
Common Topics
1. Chord of Contact : T = 0
2. Chord with given midpoint : T = S1
Director Circle
In case of parabola, Directrix is also
the director circle.
3. Pair of Tangents : S.S1 = T2
Properties of Parabola
1. Semi latus rectum of the parabola y2 = 4ax, is
the harmonic mean between segments of any
focal chord of the parabola.
2. The portion of a tangent to a parabola cut off
between the directrix & the curve subtends a
right angle at the focus.
1.
2.
3.
4.
3. The tangents at the extremities of a focal
chord intersect at right angle on the directrix,
and hence a circle on any focal chord as
diameter touches the directrix.
4. Foot of perpendicular from focus on any
tangent lie on the tangent at the vertex. Also a
circle on any focal radii of a point P (at2, 2at) as
diameter touches the tangent at the vertex
Properties of Parabola
5. The area of the triangle formed by three points
on a parabola is twice the area of the triangle
formed by the tangents at these points.
6. At any point P if tangent is drawn at parabola
meet the axis at T and normal to parabola meet
axis on N, then ST =SN =SP where S is focus.
All the rays parallel to the axis of parabola
after reflecting from internal surface of parabolic
mirror always passes through focus of parabola.
5.
6.
7. Length of subtangent at any point of y2 = 4ax
is twice the abscissa of that point and
subnormal is always constant and is equal to
semi LR.
7.