A line passes throughthe point P(h,k) is parallel to the x-axis. It forms a triangle with the linesy=x and y=x+2 of area 4h2(4(h)square) then find the locus of the point.

y=x andy=x+2 are two parallel lines ......so the triangle cannot be formed by using these two line and other....

so the given question is wrong

 LOOK IT IS VERY EASY I WILL TELL YOU THE METHOD YOU TRY IT ON YOURSELF IF YOU DONT GET IT THEN REPLY TO ME IF YOU GET IT THEN IT IS GUD...

  NOW YOU CAN FIND THE EQUATION OF LINE PASSING THROUGH (h,k) WITH SLOPE 0 SINCE IT IS PARALLEL  TO X AXIS WHICH WOULD BE (Y-k)=0(X-h)

  THEN SINCE THE LINE INTERSECTS TWO FORM A TRIANGLE . FIND THE COORDINATES OF POINT OF INTERSECTION OF THE LINES THEN YOU WILL HAVE THE THREE COORDINATES OF THE TRIANGLE NOW ARE OF THE TRIANGLE IS SUPPOSE YOU GET THE COORDINATES AS (a,b),(c,d),(e,f). THEN THE AREA IS 1/2 * MODULUS OF THE DETERMINANT 

WHICH COMES OUT TO BE 1/2 * [(ad+cf+eb)-(bc+de+af)] and YOU KNOW THE AREA EQUATE IT TO  4h²  YOU WILL THEN GET A EQUATION ''h'' and ''k''  THEN REPLACE ''h'' by ''x'' and ''k'' by ''y'' YOU WILL GET THE EQUATION OF THE LOCUS 

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