Find the equation of circum-cirle of the triangle formed by the straight lines given the following
pls give relevant answer
Answers
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 = 1/2
put the value in equation (3)
1/2 + x = 0
=> x = -1/2
so, A(-1/2 , 1/2)
2x + 3y = 5
2x + 2y = 0
_________
y = 5
put the value in equation (3),
x = -5
i.e, C(-5 , 5)
5x − 3y = −4
2x + 3y = 5
_________
7x = 1
=> x = 1/7
put the value in equation (1)
5.(1/7) - 3Y = -4
=> Y = 11/7
I.e B(1/7 , 11/7)
Equation of circles is
x^2 + y^2 + 2gx + 2fy + c = 0 _____(4)
put, A(-1/2 , 1/2), B(1/7 , 11/7) and C(-5 , 5) conrequently,
1/4 + 1/4 - g + f + c = 0
=> - g + f + c = - 1/2. ____(5)
1/49 + 121/49 + 2/7 g + 22/7 f + c = 0
=> 14 g + 154 f + 7c = - 122. ____(6)
25 + 25 − 10g + 10f + c = 0
=> − 10g + 10f + c = −50. ____(7)
multiply 10 with equation (5) and then Subtraction equation (7) from it we get,
10g + 10f + 10c = −5
− 10g + 10f + c = −50.
_________________
9c = 45
so, C = 5
put value of C in equation (5)
- g + f = -1/2 - 5
=> -2g + 2f = 7. ____(8)
put value of C in equation (6)
14 g + 154 f + 35 = - 122.
=> 14 g + 154 f = - 157. ___(9)
multiply 7 with equation (8) and then Subtraction equation (9) from it we get,
- 14 g + 14 f = 49
14 g + 154 f = - 157
________________
168f. = 206
=> f = 103/84
so, g = 397/84
∴ Now, Equation of circle ⇒
84x^2 + 84y^2 + 794x + 206y + 420 = 0
or, 42x^2 + 42y^2 + 397x + 103y + 210 = 0
(ans.)
Answer:
Oh you r in 12 then y u were saying that u came from clg?
Myself Siva from Tamilnadu
Class 11 and thank you very much for thanking my answers☺