the numerial value of the area of triangle formed by a moving line on the coordinate axes is 2c^2..find locus of the middle point of the portion of line intercepted between axes.❓

sol:let the line be x/a+y/b=1 clearly the 3 vertices of triangle will be (0,0);(a,0)and (0,b).The area will be found by determinant and will be equal to ab/2.Now area is also given 2c^2.so,ab/2=2c^2 or ab=4c^2now the middle point of the interceped line is given by(a/2,b/2)we have to found its locus it will be a/2×b/2=4c^2÷4 or a/2×b/2=c^2Now we replace (a/2,b/2) by (x,y) as we are asked locus so we get xy=c^2Hence required locus is xy=c^2I tried my best;hope it would help you if yes let m