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Vidaara.orgClass 11 · Mathematics
CodeVID-M11-10-PAR-01
Parabola — Assignment
Chapter: Conic Sections
Topic: Parabola
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
The focus of $y^2=4ax$ is:
  • A.$(0,a)$
  • B.$(a,0)$
  • C.$(-a,0)$
  • D.$(0,-a)$
2.
The directrix of $y^2=4ax$ is:
  • A.$x=a$
  • B.$x=-a$
  • C.$y=-a$
  • D.$y=a$
3.
The vertex of $y^2=4ax$ is:
  • A.$(a,0)$
  • B.origin
  • C.$(0,a)$
  • D.$(-a,0)$
4.
For $x^2=4ay$, the focus is:
  • A.$(a,0)$
  • B.$(0,a)$
  • C.$(0,-a)$
  • D.$(-a,0)$
5.
The axis of $y^2=4ax$ is the:
  • A.y-axis
  • B.x-axis
  • C.line $y=x$
  • D.directrix
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Find the focus of $y^2=12x$.
7.
Find the directrix of $y^2=8x$.
8.
Find the length of the latus rectum of $y^2=4ax$.
9.
Find the focus of $x^2=16y$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
For $y^2=20x$, find the focus, directrix and latus rectum.
11.
Find the equation of the parabola with vertex at the origin and focus $(3,0)$.
12.
For $x^2=-8y$, find the focus and directrix.
13.
Find the vertex and axis of $y^2=-4x$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Find the equation of the parabola with vertex at the origin, axis along the y-axis, passing through $(4,2)$.
15.
Find the focus, directrix and length of the latus rectum of $y^2=-12x$.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $(a,0)$
  2. (B) $x=-a$
  3. (B) origin
  4. (B) $(0,a)$
  5. (B) x-axis
Section B — Short Answer (2 marks)
  1. $(3,0)$.
  2. $x=-2$.
  3. $4a$.
  4. $(0,4)$.
Section C — Short Answer (3 marks)
  1. Focus $(5,0)$, directrix $x=-5$, latus rectum $20$.
  2. $y^2=12x$.
  3. Focus $(0,-2)$, directrix $y=2$.
  4. Vertex origin; axis the x-axis (opens left).
Section D — Long Answer (5 marks)
  1. $x^2=8y$.
  2. Focus $(-3,0)$, directrix $x=3$, latus rectum $12$.
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