Question

5. Find the equation of the circum circle of the triangle formed by the straight lines given in

each of the following.

i) 2x + y = 4; x + y = 6; x + 2y = 5

ii) 5x-3y+4=0;2x+3y-5=0; X+y=0
iii) x-y-2=0;2x-3y+4 =0 ,3x-y+6=0​

Answer 1

Step-by-step explanation:

Let AB⇒5x−3y+4=0 ......... (1)

BC⇒2x+3y−5=0 ......... (2)

CA⇒x+y=0 ........... (3)

5x−3y=−4

−5x+5y=0

____________

−8y=−4⇒y=

2

1

∴

A(−

2

1

,

2

1

)

2

1

+x=0⇒

x=−

2

1

2x+3y=5

2x+2y=0

____________

y=5

a=−5

∴C(−5,5)

5x−3y=−4

2x+3y=5

___________

7x=1⇒

x=

7

1

∴

(

7

1

,

7

11

)

5(

7

1

)−3y=−4⇒

y=

7

11

Equation of circles is x

2

+y

2

+2gx+2fy+c=0 .......... (4)

Putting A(−

2

1

,

2

1

),B(

7

1

,

7

11

) and c(−5,5) conrequently.

4

1

+

4

1

−g+f+c=0⇒

−g+f+c=−

2

1

..... (5)

49

1

+

49

121

+

7

2

g+

7

22

f+c=0⇒

14g+154f+7c=−122

.......... (6)

25+25−10g+10f+c=0⇒

−10g+10f+c=−50

....... (7)

10gg+10f+10c=−5

−10g+10f+c=−50

_________________

9x=45⇒

c=5

−g+f=−

2

1

−5=−

2

7

⇒

−2g+2f=−7

14g+154f+35=−122⇒

14g+154f=−157

−14g+14f=−49

14g+154f=−157

_______________

168f=−206⇒

f=

84

103

g=

84

397

∴ Equation of circle ⇒84x

2

+84y

2

+794x+206y+420=0

or

42x

2

+42y

2

+397c+103y+210=0