RD Sharma Solutions for Class 11-commerce Maths CBSE Chapter 24: The Circle

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

The Circle Exercise Ex. 24.2

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

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