Question

Find the equation of the circle passing through the (5,7),(8,1),(1,3)

Answer 1

Answer:

Step-by-step explanation:

solving this  by family of circles method

taking 5,7 and 8,1 as diametric end points

x-5*x-8 + y-7*y-1

equation of line joining points or else equation of diameter

2x+y=17

by family of circles

x-5*x-8 + y-7*y-1 + lamda(2x+y-17) = 0

1,3 satisfies above

28-8 + lamda(-14) = 0

lamda = 7/10

therefore equation of circle

x-5*x-8 + y-7*y-1 + 7/10(2x+y-17) = 0

perpendicular bisector method

perpendicular bisector of 1,3 and 8,1

7x-2y=55/2

14x-4y=55

perpendicular bisector of 1,3 and 5,7

x+y=8

intersection of 14x-4y=55 and x+y=8 gives centre of circle

and centre to one of the coordinate gives radius