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if the straight line 2x+3y=1, x+ 2y=1 and ax + by =1 form a triangle with origin as orthocenter , then (a,b) is

if the straight line 2x+3y=1, x+ 2y=1 and ax + by =1 form a triangle with origin as orthocenter , then (a,b) is

Grade:12th pass

1 Answers

Arun
25758 Points
3 years ago
solving first two lines you get the point opposite to the side formed by ax+by-1=0 .the point i s P1(-1,1).

since the origin is the orthocentre the product of slope joining P1 and oigin should be perpendicular to the variable line.

from the above condition u get the condition that a= -b .

using second and third line ,the line passing throught the point on intersection and origin is x(a-1)+y(b-2)=0 .this line is perpendicular to the first  line. this gives you the second condition u need to get values of a and b 

a=8 , b =-8
 

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