The equation to the circle circumscribing the triangle formed by the lines x-y-2=0, 2x - 3y + 4 = 0 3x-y+6=0
Answers
Answer:
x^2+y^2–24x+16y-52=0,Answer.
Step-by-step explanation:
x-y-2=0. . ………….(1)
2x-3y+4=0…………..(2)
3x-y+6=0………………..(3)
On solving eq.(1) & (2)
x=10 , y=8 , A(10,8)
On solving eq.(2) & (3)
x=-2 , y = 0 , B(-2,0)
On solving eq.(3) & (1)
x=-4 , y = -6 , C(-4,-6).
Let the eq.of cir cle is:-
x^2+y^2+2gx+2fy+c=0………………….(4)
The circle passes through point (10,8).(-2,0) and (-4,-6).
100+64+20g+16f+c=0
20g+16f+c=-164………….(5)
4–4g+c=0
-4g+c= -4………………….(6)
16+36–8g-12f+c=0
-8g-12f+c=-52………………….(7)
Multiply eq.(5) by3, and (7)by 4.
60g+48f+3c=-492……………..(8)
-32g-48f+4c=-208…………………(9)
On adding
28g+7c= -700
4g+c=-100……………..(10)
On solving eq.(6) & (10)
g=-12 , c =-52 .
put g=-12 and c=-52 in eq.(7)
-8×(-12)-12f-52=-52
96–12f=0 => f=8 .
put g=-12 ,f =8 and c = -52 in eq.(4)
x^2+y^2–24x+16y-52=0 ,Answer.
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