CBSE Class 11-science Answered
Let the equation of the curve when origin is at (0, 0) is
a X2 + b X Y + c Y2 + d X + e Y + f = 0 ..................... (1)
when origin is shifted to (2, 3 ) , then above equation of curve with respect to new origin becomes
a ( X - 2 ) 2 + b (X-2) ( Y - 3 ) + c ( Y-3)2 + d (X - 2 ) + e ( Y - 3 ) + f = 0
a X2 + b X Y + c Y2 + (-4a-3b+d ) X + (-2b-6c+e ) Y + ( 4a + 6b +9c-2d-3e+f ) = 0 .....................................(2)
Let us compare the above eqn.(2) with the given equation
x2 + 3 x y - 2 y2 + 17 x -7 y - 11 = 0 ............................................. (3)
By comparing the respective coefficients of eqn.(2) and eqn.(3) , we get
a = 1 ; b = 3 ; c = -2
-4a -3b+d = 17
By substituting a and b in above equation, we get d = 30 ;
-2b-5c+e = -7
By substituting b and c in above equation, we get e = -11 ;
( 4a + 6b +9c-2d-3e+f ) = -11
By substituting a, b, c , d and e in above equation, we get f = 12 ;
Hence equation of curve before shifting th origin is
X2 + 3 X Y - 2 Y2 + 30 X - 11 Y + 12 = 0