Question

find the equation of the circle which passes through the point A(3,-2) B(4,5) C(-6,-3)​

Answer 1

Answer

(- 63/31, 71/31)

Step-by-step explanation:

3.. ..-2.. ..13.. ..3

4.. …5.. …41.. ..4

-6.. ..-3.. .45.. ..-6

3..…—2… .13.. ..3

x∆y = 23+18+ 21 = 62

y∆SS = —147+ 348 +51 = 252

SS∆y = —71 —426 + 213 = 284

Circumcentre : (—63/31, 71/31)

Radius : = 205/31

.

Aliter :

We write the three points as :

.

A : (x-3)^2 + (y+2)^2 = 0

B : (x-4)^2 + (y-5)^2 = 0

C : (x+6)^2 + (x+3)^2 = 0

A- B is x +7y = 14, B-C is 5x+4y + 1 = 0

These two meet at (- 63/31, 71/31), our circumcentre.