the circumcentre of a triangle formed by  the line xy+2x+2y=0 and x+y+2=0 is?

Asked by akanshakhanna91 | 29th Jun, 2015, 09:31: PM

Expert Answer:

E q u a t i o n space o f space p a i r space o f space l i n e s space i s space g i v e n space a s x y plus 2 x plus 2 y plus 4 equals 0 R e w r i t i n g space t h e space a b o v e space e q u a t i o n comma space w e space h a v e comma x open parentheses y plus 2 close parentheses plus 2 open parentheses y plus 2 close parentheses equals 0 rightwards double arrow open parentheses x plus 2 close parentheses open parentheses y plus 2 close parentheses equals 0 rightwards double arrow x plus 2 equals 0 space a n d space y plus 2 equals 0 rightwards double arrow x equals negative 2 space a n d space y equals negative 2 O b s e r v e space t h e space f o l l o w i n g space g r a p h space o f space t h r e e space l i n e s comma x equals negative 2 comma space y equals negative 2 space a n d space x plus y plus 2 equals 0
T h u s comma space t h e space t r i a n g l e space A B C space i s space a space r i g h t space t r i a n g l e. H e n c e space t h e space c i r c u m c e n t r e space o f space t h e space t r i a n g l e space i s space t h e space m i d p o i n t space o f space t h e space h y p o t e n u s e. T h e r e f o r e comma space D open parentheses negative 1 comma space minus 1 close parentheses comma space t h e space m i d p o i n t space o f space A space a n d space C comma space i s space t h e space c i r c u m c e n t r e space o f space t h e space t r i a n g l e space A B C.

Answered by Vimala Ramamurthy | 1st Jul, 2015, 10:00: AM