Parabola Flashcards
For parabola e=?
1
Parabola of type y^2=4ax
Parabola is in 1st and 4th quadrant
y^2=-4ax
Parabola is in 2nd and 3rd quadrant
x^2=4ay
Parabola is in 1st and 2nd quadrant
x^2=-4ay
Parabola is in 4th and 3rd quadrant
Length of Latus rectum
4a
Position of a point P=(x1,y1)
When substituting in y^2 -4ax
If
P=0 on parabola
P>0 outside parabola
P
For 2 points
If
c=a/m. Real and coincident
c>a/m real and distinct
c<a></a>
Condition of tangency
c=a/m
Equation of tangent
y=mx + c
Equation of tangent for
y^2=4ax
y=mx + a/m
Point of contact
a/m^2 , 2a/m
Equation of tangent for
y^2 = -4ax
y= mx -a/m
Point of contact
-a/m^2, -2a/m
Equation of tangent for
x^4ay
y=mx - am^2
Condition of tangency => c=-am^2
Point of contact
(2am,am^2)
Equation of tangent for
x^2=-4ay
y=mx+am^2
Point of contact
-2am, -am^2
If line lx+my+n=0 touches
y^2=4ax
nl=am^2
If line xcos@+ysin@=p touches y^2=4ax
pcos@ +asin^2@=0
Director circle for parabola is
It’s directrix
Sum of slope of 3 normals at conormal point is
0
Sum of ordinates of 3 normals at the conormal point is
0
Number of normals that can be drawn from a point to parabola
3
If 3 normals are drawn from a point (h,k) to parabola y^2=4ax then
h>2a
Length of a side of an inscribed triangle in the parabola y^2=4ax is
8a(3)^1/2
Equation of a Parabola whose axis is parallel to X axis
x= Ay^2 + By +C
Equation of a Parabola whose axis is parallel to Y axis
y= Ax^2 + Bx + C
Area of a triangle formed by 3 points on parabola is
Twice the area of triangle formed by tangents at those points
Angle of intersection of 2 parabolas
tan@ = (3/2) [(ab)^1/3/((a^2)^1/3 + (b^2)^1/3)
Equation of common tangents to parabola
y^2=4ax and x^2=4ay
(A)^1/3x + (b)^1/3y + ((a^2)(b^2))^1/3=0
Diameter
It’s the locus of midpoint of parallel chords of parabola
Equation -> y=2a/m
Where m is the slope of chords
