Question

find the point to which the origin is to be shifted so that the point (3,0) may change to (2,-3) ?​

Answer 1

Answer:

Sol. i) New origin = ( )( ) 3, 4 , − = h k

∴ =− =− X xhY yk ,

= x -3 = y +4

The original equation of ( ) () 2 2 X Y + = 4 is ( )( ) 2 2

x y − ++ = 3 44

2 2

xx yy − ++ + + = 6 9 8 16 4

2 2 ∴+−++= xy xy 6 8 21 0

ii) New origin = ( )( ) h k, 1,2 = −

X xh Y yk =− =− ,

= x + 1 = y – 2

The original equation of 2 2 X Y + += 2 16 0

()( ) 2 2

x y + + − += 1 2 2 16 0

2 2

xx yy + ++ − ++ = 2 1 2 8 8 16 0 ⇒ 2 2

x y xy + +−+= 2 2 8 25 0