Vidaara.orgClass 11 · Mathematics
CodeVID-M11-10-ELH-01
Ellipse & Hyperbola — Assignment
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 standard ellipse is:
- A.$\tfrac{x^2}{a^2}+\tfrac{y^2}{b^2}=1$
- B.$\tfrac{x^2}{a^2}-\tfrac{y^2}{b^2}=1$
- C.$x^2+y^2=r^2$
- D.$y^2=4ax$
2.
For an ellipse, the eccentricity is:
- A.$=1$
- B.$<1$
- C.$>1$
- D.$=0$
3.
For a hyperbola, the eccentricity is:
- A.$<1$
- B.$=1$
- C.$>1$
- D.$=0$
4.
For an ellipse, $c^2=$
- A.$a^2+b^2$
- B.$a^2-b^2$
- C.$b^2-a^2$
- D.$a^2$
5.
The standard hyperbola is:
- A.$\tfrac{x^2}{a^2}+\tfrac{y^2}{b^2}=1$
- B.$\tfrac{x^2}{a^2}-\tfrac{y^2}{b^2}=1$
- C.$x^2+y^2=1$
- D.$x^2=4ay$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Find $a$ and $b$ for $\tfrac{x^2}{25}+\tfrac{y^2}{9}=1$.
7.
Find the eccentricity of $\tfrac{x^2}{25}+\tfrac{y^2}{9}=1$.
8.
Find the foci of $\tfrac{x^2}{25}+\tfrac{y^2}{9}=1$.
9.
Find $a$ and $b$ for $\tfrac{x^2}{16}-\tfrac{y^2}{9}=1$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Find the foci and eccentricity of the ellipse $\tfrac{x^2}{16}+\tfrac{y^2}{9}=1$.
11.
Find the lengths of the major and minor axes of $\tfrac{x^2}{36}+\tfrac{y^2}{16}=1$.
12.
Find the foci of the hyperbola $\tfrac{x^2}{9}-\tfrac{y^2}{16}=1$.
13.
Find the eccentricity of the hyperbola $\tfrac{x^2}{16}-\tfrac{y^2}{9}=1$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Find the equation of the ellipse with foci $(\pm3,0)$ and a vertex at $(5,0)$.
15.
Find the eccentricity, foci and length of the latus rectum of $9x^2-16y^2=144$.
Answer Key
Section A — Multiple Choice Questions
- (A) $\tfrac{x^2}{a^2}+\tfrac{y^2}{b^2}=1$
- (B) $<1$
- (C) $>1$
- (B) $a^2-b^2$
- (B) $\tfrac{x^2}{a^2}-\tfrac{y^2}{b^2}=1$
Section B — Short Answer (2 marks)
- $a=5,\ b=3$.
- $\tfrac45$.
- $(\pm4,0)$.
- $a=4,\ b=3$.
Section C — Short Answer (3 marks)
- Foci $(\pm\sqrt7,0)$, $e=\tfrac{\sqrt7}{4}$.
- Major $12$, minor $8$.
- $(\pm5,0)$.
- $\tfrac54$.
Section D — Long Answer (5 marks)
- $\tfrac{x^2}{25}+\tfrac{y^2}{16}=1$.
- $e=\tfrac54$, foci $(\pm5,0)$, latus rectum $\tfrac92$.
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