Class 11 Maths Chapter 10 Conic Sections – Exercise 10.1 NCERT Solutions

Introduction

Exercise 10.1 introduces the circle as a special case of conic sections. You will learn the definition, standard equation, and how to solve problems involving circles in coordinate geometry. This exercise builds the foundation for ellipse, parabola, and hyperbola in later sections.

Key Concepts

1. Definition of Circle: Set of all points equidistant from a fixed point (center).

2. Standard Equation of Circle: With center $(h,k)$ and radius $r$:

$$(x-h{)}^2+(y-k{)}^2=r^2$$

3. Circle with Center at Origin:

$$x^2+y^2=r^2$$

4. General Equation of Circle:

$$x^2+y^2+2gx+2fy+c=0$$

Center = $(-g,-f)$, Radius = $\sqrt{g^2+f^2-c}$.

NCERT Questions with Solutions (10)

Q1. Find equation of circle with center (0,0) and radius 5.

$$x^2+y^2=25$$

Q2. Find equation of circle with center (2,3) and radius 4.

$$(x-2{)}^2+(y-3{)}^2=16$$

Q3. Find equation of circle with center (-1,2) and radius 3.

$$(x+1{)}^2+(y-2{)}^2=9$$

Q4. Find equation of circle with center (0,0) and radius $\sqrt{13}$.

$$x^2+y^2=13$$

Q5. Find equation of circle with center (4,-3) and radius 5.

$$(x-4{)}^2+(y+3{)}^2=25$$

Q6. Find center and radius of circle $x^2+y^2-4x+6y-12=0$.

$$x^2-4x+y^2+6y=12$$

Completing squares:

$$(x-2{)}^2+(y+3{)}^2=25$$

Center = (2,-3), Radius = 5.

Q7. Find center and radius of circle $x^2+y^2+2x-4y+1=0$.

$$(x+1{)}^2+(y-2{)}^2=4$$

Center = (-1,2), Radius = 2.

Q8. Find equation of circle with diameter endpoints (1,2) and (3,4). Center = $(\frac{1+3}{2},\frac{2+4}{2})=(2,3)$. Radius = $\frac{\sqrt{(3-1{)}^2+(4-2{)}^2}}{2}=\frac{\sqrt{8}}{2}=\sqrt{2}$. Equation:

$$(x-2{)}^2+(y-3{)}^2=2$$

Q9. Find equation of circle passing through (1,0), (0,1), and center (0,0). Radius = distance from origin to (1,0) = 1. Equation:

$$x^2+y^2=1$$

Q10. Find equation of circle with center (2,1) passing through (5,5). Radius = $\sqrt{(5-2{)}^2+(5-1{)}^2}=\sqrt{9+16}=5$. Equation:

$$(x-2{)}^2+(y-1{)}^2=25$$

FAQs (10)

1. What is circle in coordinate geometry? Locus of points equidistant from center.

2. What is standard equation of circle? $(x-h{)}^2+(y-k{)}^2=r^2$.

3. What is general equation of circle? $x^2+y^2+2gx+2fy+c=0$.

4. How to find center from general equation? $(-g,-f)$.

5. How to find radius from general equation? $\sqrt{g^2+f^2-c}$.

6. What is circle with center at origin? $x^2+y^2=r^2$.

7. Can circle have negative radius? No, radius is non‑negative.

8. What is diameter of circle? Twice the radius.

9. What is locus definition of circle? Set of points equidistant from fixed point.

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

Conclusion

Exercise 10.1 has 10 solved questions and 10 FAQs that strengthen your understanding of circles 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 10.1 NCERT Solutions