If P ( ) and Q ( 2 + ) are two points on the ellipse x^2 a^2 + y^2 b^2 =1 and the locus of midpoint of PQ is x^2 ^2 + y^2 ^2 =1 , then a+b + =

Step-by-step solution

Given two points P ( ) and Q ( 2 + ) are on the ellipse. Hence, P =( a , b ), Q =(- a , b ) now mid point of P Q aligned & = ( a - a 2 , b + b 2 ) & x a = - 2 and 4 ~b = + 2 aligned On squaring and adding we get aligned & x ^2 a ^2 + y ^2 ~b ^2 = 1 2 ( Given as x ^2 ^2 + y ^2 ^2 =1 ) & x ^2 ( a 2 )^2 + y ^2 ( b 2 )^2 =1 & = 9 2 , = b 2 & a + b + = a + b 1 2 ( a + b ) = 2 aligned