Parabola

Question 1

e value of parabola

Answer 1

e=1, h^2=ab

Question 2

Standard Parabola

Answer 2

y^2=4ax

Question 3

Axis of parabola

Answer 3

Line passing through focus and perpendicular to the directrix

Question 4

Vertex

Answer 4

Point of intersection of parabola and axis

Question 5

Foot of directrix

Answer 5

Point of intersection of directrix and axis

Question 6

Double ordinate

Answer 6

Chord of the parabola perpendicular to the axis

Question 7

Focal Chord

Answer 7

Chord of the parabola passing through the focus

Question 8

Latus Rectum

Answer 8

Double ordinate passing through focus
Focal chord perpendicular to the axis

Question 9

Ends of LR

Answer 9

(a, ±2a)

Question 10

Length of LR

Answer 10

4a

Question 11

Parametric Coordinates

Answer 11

at^2, 2at

Question 12

Chord Equation

Answer 12

2x - (t1+t2)y + 2at1t2

Question 13

If it is a focal chord, then what is the conditions on parametric coordinates?

Answer 13

t1t2=-1

Question 14

Length of focal chord

Answer 14

a(t+1/t)^2

Question 15

Conditions of tangency of parabola

Answer 15

c=a/m

Question 16

Point Form Tangent equation

Answer 16

yy1=2a(x+x1)

Question 17

Slope Form Tangent equation

Answer 17

y = mx+a/m

Question 18

Parametric Form Tangent equation

Answer 18

yt = x+at^2

Question 19

POI of tangents at t1 and t2

Answer 19

at1t2, a(t1+t2)

Question 20

Point Form of Normal

Answer 20

y-y1=-y1/2a(x-x1)

Question 21

Parametric Form of Normal

Answer 21

y +xt = 2at + at^3

Question 22

Slope Form of Normal

Answer 22

y=mx-2am-am^3

Question 23

Director circle for a parabola

Answer 23

Directrix

Question 24

Conditions of normality

Answer 24

c = -2am-am^3

Question 25

POI of normals at t1 and t2

Answer 25

a(t1^2+t2^2+t1t2+2), -at1t2(t1+t2)

Question 26

If the normal at t1 meets the parabola again at t2, then the relation

Answer 26

t2=-t1-2/t1

Question 27

Equation of normal from any point

Answer 27

am^3+m(2a-h)+k=0

Question 28

Co-normal points

Answer 28

Foot of the normals of three concurrent normals

Question 29

Sum of ordinates of three co-normal point is

Answer 29

0