Class 11 Maths Chapter 10 Conic Sections – Exercise 10.2 NCERT Solutions

Introduction

Exercise 10.2 introduces the parabola as a conic section. You will learn its definition, standard equations, and properties. Problems focus on finding equations of parabolas, identifying focus, directrix, and axis, and solving coordinate geometry questions involving parabolas.

Key Concepts

1. Definition of Parabola: Locus of a point equidistant from a fixed point (focus) and a fixed line (directrix).

2. Standard Equations of Parabola:

   • Opening right:

$$y^2=4ax$$

• Opening left:

$$y^2=-4ax$$

• Opening upward:

$$x^2=4ay$$

• Opening downward:

$$x^2=-4ay$$

3. Key Elements:

   • Vertex: (0,0) in standard form.

   • Focus: (a,0) or (0,a) depending on orientation.

   • Directrix: line opposite to focus.

   • Axis: line of symmetry.

NCERT Questions with Solutions (10)

Q1. Find equation of parabola with vertex at origin and focus (2,0).

$$y^2=4ax,a=2⟹y^2=8x$$

Q2. Find equation of parabola with vertex at origin and focus (-3,0).

$$y^2=-12x$$

Q3. Find equation of parabola with vertex at origin and focus (0,4).

$$x^2=16y$$

Q4. Find equation of parabola with vertex at origin and focus (0,-5).

$$x^2=-20y$$

Q5. Find equation of parabola with vertex at origin and focus (1,0).

$$y^2=4x$$

Q6. Find equation of parabola with vertex at origin and focus (0,2).

$$x^2=8y$$

Q7. Find equation of parabola with vertex at origin and focus (-2,0).

$$y^2=-8x$$

Q8. Find equation of parabola with vertex at origin and focus (0,-3).

$$x^2=-12y$$

Q9. Find equation of parabola with vertex at origin and focus (0,1).

$$x^2=4y$$

Q10. Find equation of parabola with vertex at origin and focus (5,0).

$$y^2=20x$$

FAQs (10)

1. What is parabola? Locus of point equidistant from focus and directrix.

2. What is standard equation of parabola? $y^2=4ax$ or $x^2=4ay$.

3. What is vertex of parabola? Point where parabola turns, usually origin in standard form.

4. What is focus of parabola? Fixed point defining parabola.

5. What is directrix of parabola? Fixed line opposite to focus.

6. What is axis of parabola? Line of symmetry through vertex and focus.

7. Can parabola open in any direction? Yes, depends on equation sign.

8. What is parameter $a$? Distance from vertex to focus.

9. What is latus rectum? Line through focus perpendicular to axis, length = $4a$.

10. Why is this exercise important? It builds foundation for ellipse, hyperbola, and applications in physics.

Conclusion

Exercise 10.2 has 10 solved questions and 10 FAQs that strengthen your understanding of parabolas in coordinate geometry. This builds the foundation for other conic sections in Class 11 Maths.

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New Syllabus-Class 11 Maths Chapter 10 Conic Sections – Exercise 10.2 NCERT Solutions