RÜX

PARAMOLA
The set ofll oints in aplane that Me vudisaul run aOved line and fixed pont(nt m
ne
line) is

) Straight line 2)Parabola }) Pair of straight ines 4)Cirele

Aparabola is the set of all points in a plane thal are cuuidistant from a fixed line and a
oint (no\on the line) in the plane. Then fixcd ine
is called
I) Directrix 2) Focus 3)Latus rectum 4)Axis

Aparabola is the sct of all points in aplane that are cyuidistant from afixed line and afixed
point(not on the linc) in the plane. Then fixced point is called
1) Dirèctrix 2) Focus 3)Latus rectum 4) Axis

4. Aline through the focus and perendicular to the directrix 0N called

1) Directrix 2) Focus 3) Latas rectum 4)Axis

5. The point of intersection of parabola with the axis is called

1)Vertex 2) Focus 3) Origin 4) Noneof theabove

Thecquation of a parabola is sinplest ie the vertex is at

I)Vertex 2) Focus 3) Origin 4) Noueof the above
STANDARD EQUATIONOF PARAB0LA

7. The equation of' parabolawhose vertex is at the origin, axis of the parabola is positive X-axis
and focus at (u,0) is

1) y' 4ax 2) y'-4ua 3) duy 4)N4ay

8 The equation of parabolawhosc vertex is at the origin, axis of the parubola is negative N-axis
and focus at (- u,0) is

1) y' 4ax 2) y' 4uN 3)'4uy 4)N4ay

parabola is negative y-axiN
9 The cyuation of parabola whose vertex 0N l lhe origin, usis of the
und focus at (0, a) is
2) y'-4ur 3)ay 4)duy
) y'4ax

(69)
 The cquation of parabola whose vertex is at the origin, axis of the parabola is positive y-axis
10.

and focus at (0, -a) is

3) r=4y 4) r=-4ay
) y' =4ax 2) y' =-4ar

The equation of directrix of the parabola y' =4ar(a>0) is

4) I=
2) y = -a 3) x =d

12. The equation of directrix of the parabola y' =-4ar (a>0) is

3) x=a 4)
1) y=a 2) y= -a

13. The equation of directrix of the parabola x' =4v (a>0) is

) y =a 2) y= -a 3) x=d

14. The equation of directrix of the parabola x= -4ay (u >0) is

) y= a 2) '= -a 3) =l

15. The equation of parabola whose focus (a,0) and cquation of drectrix

)=4a 2) x=tav 3) y = tx

I6. The equation of parabola whose focus (a.0) and equation of directri -B

3) =ter 4) = -4E
I) x=4ay 2) x=-4av

17. The equation of' parabola whose tocus (0,a) and equation of directr)=d S

2) =4 3) =4ut 4) =ar
Dx=4a

I8.
The equation of parabola whose focus (0.a) and equation of directrix = -u iS

)=4 2)x=a 3) =4ar 4) = 4ar

LATUS RECTUM

through the focus and whose end

19. A line segment perpendicular to the axis of the parabola,
points lie on the parabola is called
1)Directrix 2) Focal chord 3) Latus rectum 4)Axis

20. The length of latus rectum of the parabola y =Aar is

) 2a 2) 4a 3) a 4) 2

PROBLEMS BASED ONSTANDARD EQUATION OF PARABOLA

21 The coordinates of the focus of the parabola y' = 8x is
D(0, 2) 2)(2, 0) 3)(-2, 0) 4) (4, 0)

22 The latus rectum of the parabola y= 8x is

)4 2) 8 3) 2 4) 16

23 The equation of directrix of the parabola y' = 8x is

l)x =2 2) x=-2 3) y=2 4) y=-2

24. The coordinates ofthefocus of the parabola y 12x is

l)(0, 3) 2) (3, 0) 3)(-3, 0) 4) (4, 0)

25. The latus rectum of the parabola y 12x is

I) 4 2) 3 3) 2 4) 12
26. The equation of directrix of the parabola y'=12x is
l)x =3 2) x=-3 3) y=3 4) y=-3
27.
The coordinates of the focus of the parabola x =6y is

3)(3, 0) 4) (2, 0)

28. The latus rectum of the parabola x =6y is

1) 6 2) 8 3) 2 4) 16
 NCERT
CXÜX
of the parabola r´ =6y is
29. Ihe cquation of directrix
3) y=2 4) y=-2
2) y
the parabola x=-16y is
30. The coordinates of the focus of
3)(3, 0) 4) (2, 0)
1) (0,4) 2) (0, -4)
31. The latus rectum ofthe parabola x'=-l6y is
3) 2 4) 16
1)6 2) 8
32. The equation of directrix of the parabola x =-l6y is
I) y=4 2) y=-4 3) y=2 4) y=-2
33. The cquation ofthe parabola with focus (2,0) and directrix x =- 2 is

1)y =8x 2) y' =-8x 3) =8y 4) x' =-8y

34. The equation ofthe parabola with focus (6,0) and directrix x=-6 is
I)y =24x ) y'-24x 3) x'=24y 4) x'=-24y
35. The equation of theparabola wilh focus (0,-3) and directrix y 3 is

I) y' =12x 2) y=-12x 3) a' =12y 4) x=-12y

36. The equation of the parabola with vertex (0, 0), focus (3,0) is
1) y' =12x 2) y' =-12x 3) x =12y 4) x'=-12y
37. The equation of the parabola with vertex at (0,0) and
focus at (0, 2) is
I) x=-8y 2) y' =-8x 3) y'=12x 4) x' =8y
38. If the focus of aparabola is (0, -3)
and its directrix is y=3, then its
equation is
I) y' =12x 2) y' =-12x 3) x=12y 4) x*=-12y
39. The equation of the parabola
which is symmetric about the y-axis,
(2,-3) is and passes through the pont

l) 3x =-4y 2) 3x' =4y

3) 3y' =-4x
4) 3y' =4x
40. The equation of the parabola which is symmetric about the y-axis, and passes through the point
(5, 2) is

1)4x' =25y 2) 4x' =-25y 3) 4y² =25x 4) 4y' =-25x

41. If the parabola y² =4ax passes through the point (3, 2), then the length of its latus rectum is
2
2) 4) 4

42. If the vertex of the parabola is the point (-3, 0) and the directrix is
the line x +5=0, then its
equation is

1)y² = 8 (x + 3) 2) x² =8 (y + 3) 3) y² =-8 (x+3) 4) y² = 8 (x + 5)

APPLICATIONS

43. An equilateral triangle is inscribed in the parabola

y² 4ax whose one vertex is at the vertex of
the parabola, then the length of the side of
the triangle is.
1) 2ay3 2) 2a 3) 8av3 4)8a
44. The area of triangle formed by the lines
joining the vertex of parabola x=12y to the ends of its
latus rectum is

1) 12 sq.units 2) 16 sq.units 3) 18 sq.units 4) 24 sq.units

45. The Coordinates of apoint in first
quadrant on the parabola y² =8xwhose focal distance is 4 is.
1) (4, 2) 2) (4,-2) 3) (-2,-4)
4)(2, 4)
46. The line lr+ my+n=0with touch the
parabola Y² =4AX IF.
1) em = an 2) En = am 3) mn = al?
4) mn = a'e
 NCERT points on it t which
thc
CRÜ of the
parabola y'- 6x to
J0ining tlhe vetex
47 The cquations of the lincs
have abscissa 24 are
4) 2x y= 0
3)x ± 2y =0
2) 2y ±x =0

KEY
10
5 4 3
1 2
4 1 3
2 2 19 20
16 1718
11 12 13 14 15
3 2
2 1 4 3
4 3
28 29 30
21 22 23 25 26
1 3 2
2 4 3 2
2 2 2
38 39 40
31 34
4 1 4

41 42 43 44 4 46 47
2 3 3 2