Let P(x, y) be the mid point of the line joining (1,0) to a point on the curve y ²= | array ll x +1 & x +2 x +3 & x +5 array | . Then, locus of P is symmetrical about

Step-by-step solution

The given curve y ²= | array ll x +1 & x +2 x +3 & x +5 array | aligned & y ²=( x +1)( x +5)-( x +2)( x +3) & y ²= x ²+6 x +5- x ²-5 x -6 & y ²= x -1 which is parabola. aligned Let the parametric coordinate of parabola is Q = ( t ² 4 , t 2 +1 ) Now, given that P ( x , y ) is the mid point of AQ . P(x, y)= [ t² 4 +1 2 , t 2 +1 2 ] array ll & x = t ² 8 + 1 2 8 x = t ²+4 and & y = t 4 + 1 2 t =2(2 y -1) & 8 x =4(2 y -1)²+4 & 2 x =(2 y -1)²+1 & (2 y -1)²=(2 x -1) & 4 ( y - 1 2 )²=2 ( x - 1 2 ) & ( y - 1 2 )²= 1 2 ( x -