Parabola

Question 1

For parabola e=?

Answer 1

1

Question 2

Parabola of type y^2=4ax

Answer 2

Parabola is in 1st and 4th quadrant

Question 3

y^2=-4ax

Answer 3

Parabola is in 2nd and 3rd quadrant

Question 4

x^2=4ay

Answer 4

Parabola is in 1st and 2nd quadrant

Question 5

x^2=-4ay

Answer 5

Parabola is in 4th and 3rd quadrant

Question 6

Length of Latus rectum

Answer 6

4a

Question 7

Position of a point P=(x1,y1)

When substituting in y^2 -4ax

Answer 7

If
P=0 on parabola
P>0 outside parabola
P

Question 8

For 2 points

Answer 8

If
c=a/m. Real and coincident

c>a/m real and distinct

c<a></a>

Question 9

Condition of tangency

Answer 9

c=a/m

Equation of tangent
y=mx + c

Question 10

Equation of tangent for

y^2=4ax

Answer 10

y=mx + a/m

Point of contact
a/m^2 , 2a/m

Question 11

Equation of tangent for

y^2 = -4ax

Answer 11

y= mx -a/m

Point of contact
-a/m^2, -2a/m

Question 12

Equation of tangent for

x^4ay

Answer 12

y=mx - am^2

Condition of tangency => c=-am^2

Point of contact
(2am,am^2)

Question 13

Equation of tangent for

x^2=-4ay

Answer 13

y=mx+am^2

Point of contact
-2am, -am^2

Question 14

If line lx+my+n=0 touches

y^2=4ax

Answer 14

nl=am^2

Question 15

If line xcos@+ysin@=p touches y^2=4ax

Answer 15

pcos@ +asin^2@=0

Question 16

Director circle for parabola is

Answer 16

It’s directrix

Question 17

Sum of slope of 3 normals at conormal point is

Answer 17

0

Question 18

Sum of ordinates of 3 normals at the conormal point is

Answer 18

0

Question 19

Number of normals that can be drawn from a point to parabola

Answer 19

3

Question 20

If 3 normals are drawn from a point (h,k) to parabola y^2=4ax then

Answer 20

h>2a

Question 21

Length of a side of an inscribed triangle in the parabola y^2=4ax is

Answer 21

8a(3)^1/2

Question 22

Equation of a Parabola whose axis is parallel to X axis

Answer 22

x= Ay^2 + By +C

Question 23

Equation of a Parabola whose axis is parallel to Y axis

Answer 23

y= Ax^2 + Bx + C

Question 24

Area of a triangle formed by 3 points on parabola is

Answer 24

Twice the area of triangle formed by tangents at those points

Question 25

Angle of intersection of 2 parabolas

Answer 25

tan@ = (3/2) [(ab)^1/3/((a^2)^1/3 + (b^2)^1/3)

Question 26

Equation of common tangents to parabola

y^2=4ax and x^2=4ay

Answer 26

(A)^1/3x + (b)^1/3y + ((a^2)(b^2))^1/3=0

Question 27

Diameter

Answer 27

It’s the locus of midpoint of parallel chords of parabola

Equation -> y=2a/m

Where m is the slope of chords