AP EAMCET2016MathematicsPair of Lines
The orthocentre of the triangle formed by the lines x+y=1 and 2 y^2-x y-6 x^2=0 is
Options
- A( 4 3 , 4 3 )
- B( 2 3 , 2 3 )
- C( 2 3 , -2 3 )
- D( 4 3 , -4 3 )
Correct answer
A. ( 4 3 , 4 3 )
Step-by-step solution
Given that, x+y=1 and 2 y^2-x y-6 x^2=0 aligned & 2 y^2-4 x y+3 x y-6 x^2=0 & (2 y-3 x)+(y-2 x)=0 & 2 y+3 x and y-2 x=0 aligned Equation of sides are x+y=1,2 y+3 x=0 and y-2 x=0 Solving these equations simultaneously, we get the coordinate of the points A (0,0), B ( 1 3 , 2 3 ) and C (-2,3) Equation of altitude AD , x-y=0 ... (i) Equation of altitude CF , x+2 y= ... (ii) Since, this passes through (-2,3) -2+6= =4 So, equation of altitude CF x+2 y=4 On solving eqs. (i) and (ii), we get x= 4 3 , y= 4 3 Orthocentre of