RD SHARMA Solutions for Class 11-science Maths Chapter 24 - The Circle

Chapter 23 - The Circle Exercise Ex. 24.2

Solution 14


 

 

Solution 1(i)

Solution 1(ii)

Solution 1(iii)

Solution 1(iv)

Solution 2(i)

Solution 2(ii)

Solution 2(iii)

Solution 2(iv)

Solution 3

A space c i r c l e space p a s sin g space t h r o u g h space P left parenthesis 3 comma minus 2 right parenthesis space a n d space Q left parenthesis minus 2 comma 0 right parenthesis space a n d space h a v i n g space i t s space c e n t r e space o n space 2 x minus y equals 3.
L e t space t h e space e q u a t i o n space o f space t h e space c i r c l e space b e space x squared plus y squared plus 2 g x plus 2 f y plus c equals 0.
S i n c e space t h e space c i r c l e space p a s s e s space t h r o u g h space left parenthesis 3 comma minus 2 right parenthesis space a n d A l s o space space left parenthesis minus 2 comma 0 right parenthesis space t h e r e f o r e
9 plus 4 plus 6 g minus 4 f plus c equals 0....... left parenthesis i right parenthesis
4 plus 0 minus 4 g plus 0 plus c equals 0........ left parenthesis i i right parenthesis
A l s o space t h e space c e n t r e space o f space t h e space c i r c l e space l i e s space o n space 2 x minus y equals 3
minus 2 g plus f equals 3......... left parenthesis i i i right parenthesis
S o l v i n g space e q u a t i o n s space left parenthesis i right parenthesis comma left parenthesis i i right parenthesis space a n d space left parenthesis i i i right parenthesis comma space w e space g e t
g equals 3 over 2 comma space f equals space 6 space a n d space c equals 2
T h e r e f o r e space t h e space e q u a t i o n space o f space t h e space c i r c l e space i s
x squared plus y squared plus 3 x plus 12 y plus 2 equals 0

Solution 4

Solution 5

Solution 6

Solution 7(i)

Solution 7(ii)

Solution 7(iii)

Solution 8

Solution 9

I f space a comma space b comma space c space a r e space i n space A P comma space t h e n space b equals fraction numerator a plus c over denominator 2 end fraction
F o r space a equals 1 comma b equals space 4 comma c equals space 7 comma space fraction numerator 1 plus 7 over denominator 2 end fraction equals 4 equals b comma space t h e r e f o r e space 1 comma space 4 comma space 7 space a r e space i n space A P.
T h e space c e n t r e s space o f space t h e space t h r e e space c i r c l e s space l i e space i n space A P.

Solution 10

Solution 11

Solution 12

Solution 13

Solution 7(iv)

  

Solution 15

  

Chapter 24 - The Circle Exercise Ex. 24.1

Solution 1(i)

Solution 1(ii)

Solution 1(iii)

Solution 1(iv)

Solution 1(v)

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7(i)

Solution 7(ii)

Solution 7(iii)

Solution 7(iv)

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

 

 

Solution 17

 

 

 

Solution 18


 

 

 

Solution 19

Solution 20

Solution 21

Chapter 24 - The Circle Exercise Ex. 24.3

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 10

Solution 11

Solution 12

 

Solution 9

  

Chapter 24 - The Circle Exercise Ex. 24VSAQ

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9