If (a ,b ) is the centre of the circle passing through the vertices of the triangle formed by x+y=6 ,2x+y=4 and x+2y=5, then (a ,b ) is

Question

Accepted Answer

Correct answer: B. (b) Given, sides of triangles x+y=6 … … … … … . (i )2x+y=4 … … … . . ( ii )x+2y=5 … … … ( iii ) on solving equations find vertices, A (-2 ,8 ) ,B (7 ,-1 ) and C (1 ,2 ) Let coordinate of circumcentre be O (h ,k ) Then OA= OB= OC OA= OB ⇒OA^2=OB^2 ⇒ (h+2 )^2+ (k-8 )^2= (h-7 )^2+ (k+1 )^2 ⇒h^2+4+4h+k^2+64-16k=h^2+49-14h+k^2+1+2k … … … … ( iv ) or h-k+1=0 ⇒ OB= OC ⇒OB^2=OC^2 ⇒ (h-7 )^2+ (k+1 )^2= (h-1 )^2+ (k-2 )^2 ⇒-12h+6k+45=0 … … … … . . (v ) From eqs. (iv) and (v), we get h= 172 ,k= 192 ∴ Circumcentre ( 172 , 192 )

$If (a, b) is the centre of the circle passing through the vertices of the triangle formed by x + y = 6, 2 x + y = 4 and x + 2 y = 5, then (a, b) is$

Solution

More Hyperbola PYQs